BORIS DEBIC: Welcome,

everybody to one more Authors at Google talk. Today with us, Brian

Christian and Tom Griffiths. Their book, “Algorithms

to Live By,” is now available in all the

fine bookstores in the area and in the US and around

the world and whatnot. Brian Christian is the author

of “The Most Human Human,” a “Wall Street Journal”

bestseller, “New York Times” editor’s choice,

and “New Yorker” favorite book of the year. His writing has appeared in “The

New Yorker,” “The Atlantic,” “Wired,” the “Wall Street

Journal,” “The Guardian,” and “The Paris Review,” as

well as in scientific journals such as “Cognitive Science.” He has been translated

into 11 languages. He lives in San Francisco. Tom Griffiths is a professor

of psychology and cognitive science at UC Berkeley,

where he directs the computational

cognitive science lab. He has published more

than 150 scientific papers on topics ranging from

cognitive science psychology to cultural evolution. He has received awards from the

National Science Foundation, the Sloan Foundation,

the American Psychology Association, and the Psychonomic

Society, among others. He lives in Berkeley. So I’m not going to talk

too much about the book because we have

Peter Norvig here, who will explain

to you why this may be the– we call it the gateway

drug to computer science. Come on, Peter. PETER NORVIG: OK. So you remember Apple

had this campaign that said, think different? And I think we

realize that we all think different in some ways. Right? So we’re all nerds or

whatever you want to call us. And sometimes when you go out

with your friends and family, you realize, oh, I think

differently than them. And I think that’s what

this book is about. Boris talks about it

as a gateway drug, and I think that’s great. That’s a good way to think

about it because we’re coming up now– there’s another

hour of code thing, and we’re going to celebrate. And we’re going to try to

teach everybody to code. But learning how to draw

a rectangle on the screen and figuring out that

the third argument is the color and the first two are

the x- and the y-coordinates, that’s not really it. That doesn’t change

the way you think. I mean, that’s a

good skill, to be able to draw rectangles

and circles on the screen. But really what’s important is

being able to model the world. Jeanette Wing talks about it

as computational thinking. And I think there’s a mix

between different types of thinking. There’s this

computational thinking. There’s a mathematical thinking. There’s a statistical thinking. And we all have

some combinations of all of those things. And those skills

together, I think, are more important than

the details of the API for JavaScript objects. And this book really gets at it. It doesn’t teach

you how to code, but it teaches you how

to think in that way. And it gives you examples to

ponder about your everyday life and why it might be

important to think that way and when you can do with it. So tell us all about

it, Brian and Tom. [APPLAUSE] BRIAN CHRISTIAN:

Thank you so much, Boris and Peter, for

the introduction, and thanks to Google for the

invitation to come speak. The talk is “Algorithms

to Live By.” I’m Brian. This is Tom, in case you were

curious which of us is which. We sometimes get that question

if we’ve forgotten to introduce ourselves at the top. And the book opens

with an example that I think will be acutely,

perhaps uncomfortably, familiar to many of us

here in the Bay Area, which is looking for housing. So in a typical consumer

situation, the way you make a choice is you

consider a pool of options. You think hard about which

one you like the best. And then you go with that. But in a sufficiently

crowded real estate market, in a sufficiently competitive

market– which the Bay Area certainly

is– you don’t have the luxury of making the

decision in that way. Rather, the decision

takes the form of evaluating a sequence

of options one at a time, going to a number of

different open houses, and at each point

in time, you must make an irrevocable commitment. You either take the place that

you’re looking at right there on the spot, never knowing what

else might have been out there, or you walk away,

never to return. You have almost no chance

of going back and getting the place. This is certainly a much

more fraught setting for making a decision because

here the critical question that you have to ask yourself

is not which option to pick but how many options

to even consider. Intuitively, we have

this idea that you want to look before you leap. You don’t want to make

a premature choice. You want to get a sense

of what’s out there. But you don’t want

to hold out too long for some kind of perfect

thing that doesn’t exist And let the best

options pass you by. So our intuition

tells us that we have to strike some

kind of balance between getting a feel

for what’s out there and setting a standard and

knowing a good thing when we see it and being

ready to commit. And the story that we get

from mathematics and computer science is that this

notion of balance is, in fact, precisely correct. But our intuition

alone doesn’t tell us what that balance should be. The answer is 37%. If you want the very

best odds of finding the very best

apartment, consider exactly 37% of the pool of

options in front of you. Or alternately, you can think

of it in terms of time– 37% of your time

just calibrating. Leave your checkbook at home. If you’ve given yourself a month

for the search, in this case, that would be 11 days. After that point, be prepared

to immediately commit to the first thing you see

that’s better than what you saw in that first 37%. This is not only the

intuitively-satisfying compromise between

looking and leaping, this is the provably optimal

solution to this problem. So, for example,

if you’re committed to living in one of the painted

ladies here in San Francisco, and they have their open

houses on successive weekends, the algorithm tells you

to look at the first two, and no matter how tempting

they seem, hold tight. And then, starting

with the third one, immediately leap

for the first one better than what you

saw at the first two. Now, more broadly,

this is known as what’s called an optimal

stopping problem. And this structure

of encountering a series of options

and being forced to make a commitment one way or

another– either you’re all in or you walk away–

some people have argued that this is a structure

that describes not only things like the apartment hunt

or real estate in general. It also, many people have

argued, describes dating. You’re in a relationship,

and you have this decision of when to commit. Have you met enough people

to have a sense of who your best match really is? And so you can do some

back-of-the-envelope math and say things like, OK, the

average expected lifespan of an American is 79. 37% of that gives me 29. And this roughly

divides my romantic life into dating for fun

versus dating seriously to really evaluate for a mate. Of course, as we will see, it

all depends on the assumptions that you’re willing

to make about love. TOM GRIFFITHS: So

as you’ve seen, simple algorithms can solve

some of the problems which we actually normally think about

not as problems for computers but as problems for people. So there are a set

of problems which we have to solve just as

a consequence of the fact that our lives are lived in

finite space and finite time– so having to do things like try

and figure out how to organize our house or our closet

or our office in a way to make it most efficient

or trying to figure out how to schedule our

time so that we can do the most possible things. And we normally

think about those as being fundamentally

human problems. But really, the argument

that we make in the book is that they’re not. They have analogs

to the problems that computers have to solve. So, you know, your

computer has to figure out how to manage its space–

its space on the hard disk and its space in memory. And it also has

to figure out how to manage its time– what

it’s going to do next, what program it’s going to run. And as a consequence,

computer scientists have put a lot of thought into

coming up with good algorithms for solving those problems. So what we do in

the book is explore how taking this perspective

gives us insight into the problems that

human beings have to solve, in some cases offering us

nice, elegant, simple solutions to these problems,

like the 37% rule, in other cases giving us new

ways of thinking about how those problems might be

described in mathematical terms and given, perhaps, a kind

of quantitative analysis. So we consider a range of

different problems– so the optimal stopping problem,

which you’ve heard a little bit about, as well as a

variety of other contexts in which thinking

algorithmically actually gives us a new insight into

a human sort of problem. And what we’re going to do

today is talk about just a few of these problems. In the book, we

also talk about some of the more general

principles which go into designing

good algorithms or thinking about the

kinds of underlying ideas that are useful

when we’re trying to engage with the world

in this computational way. So the three problems that

we’re going to focus on today are optimal stopping, the

explore or exploit trade-off, and caching. And optimal stopping

you’ve already heard a little bit about. The 37% rule is

just one instance of a strategy which is useful

for solving an optimal stopping problem. It’s the solution

to a problem which is known in the mathematical

literature as the secretary problem. So the canonical set-up

for this is that you’re trying to hire a secretary. You have a pool of applicants. Each applicant comes

in and is interviewed. You don’t have a way of

evaluating the applicants except against one another. So you can only make a

judgement of how good they are based on the applicants

that you’ve seen so far. And for each person

who comes in, you have to make a

decision immediately as to whether you hire that

person or whether you dismiss them, in which case

you’ll never see them again. So this secretary

problem was first presented to the

public in the 1960s in a column that was

written by Martin Gardner. But in the book, we trace the

history of this problem back, and it turns out that

romance was at its core. So what we actually found by

doing some archival research is that the person who claims

to have originated the problem is a mathematician

called Merrill flood. And the story that

he tells about it is that his daughter,

who had just graduated from high school,

was engaging in a relationship which he and his wife

didn’t really approve of with a much older man. And so he wanted to

somehow convince her that this was a bad idea. So being a

mathematician, the way that he approached

this problem was she turned out to be taking the

minutes at a mathematics conference that Flood was

scheduled to present at. And so he went up, and

he presented this problem of a woman who’s entertaining

a series of suitors and faced with the

challenge of deciding which of those suitors’

proposals she should accept. And he didn’t actually

know the solution to the problem at that point. But he was pretty sure that

the number was larger than one. And so he was hoping that

his daughter would sort of take the message as she

was writing it down, and sort of think about how it

applied to her own situation. So as we’ve seen, the

solution to this problem turns out to be 37%. But as Brian was

saying, a lot of that depends on the

assumptions that you make. And there’s actually been

a history of mathematicians seeking love that provide some

cautionary tales and perhaps some insights into variants

on this problem, which are things that are worth

paying attention to. So one kind of

situation that you can encounter when trying

to pursue this approach is rejection. And we actually found a

story of Michael Trick, who’s an operations researcher

at Carnegie Mellon University. And he told the story of

applying the secretary problem in very much the same way

that Brian was describing– calculating the

period over which he thought he’d be searching,

working out what 37% was. And it happened that the age

at which he should switch from having fun to being serious

was precisely his current age. And so he went and

proposed to his girlfriend, who turned him down. So Trick ran into one

of the assumptions that are being made here,

which is that when you make an offer

to somebody, they should be willing to accept it. And only under

those circumstances is the 37% rule valid. If somebody is potentially

able to reject your offer, then it changes the strategy

that you should follow. And in particular, it means

that the period that you spend looking should be reduced. So, for example, if you have a

50% chance of being rejected, then you should look

at the first 25% of your potential

candidates, and then be willing to make an offer

to the first person who’s better than anybody you

saw in that first 25%. Another variant on

the secretary problem is what’s called recall. And so this is having

the opportunity to go back to somebody

who you passed over. So you can imagine your

candidates come in, but rather than dismissing them meaning

that you’ll never see them again, dismissing

them just decreases the chance that you’ll be

able to go back to them. Or in the dating

setting, basically, breaking up with somebody

means that maybe there’s a chance that they’d

take you back later on. So there’s actually

a mathematician who experienced exactly

this phenomenon. This is the astronomer

Johannes Kepler, who after his first wife died went

through an extended period of courting various

women, trying to sort of evaluate and come up

with the person who he thought was going to be the very

best person for him. And so over an

extended period, he ended up interacting

with 11 women. And having sort of explored

those possibilities, he decided, getting to

the end of that process, that number five, who

he’d previously dismissed, was actually the

best one for him. So he went back, and he

made an offer to her. And it turned out she hadn’t

accepted any other proposals in the meantime. And so luckily, they

were able to be married and had a happy

marriage together. So this possibility– that

you can actually go back to somebody, and they

can still say yes– changes where you should

set your threshold again. So in this case, it

makes it something where you should spend a

little longer looking around. So, for example, if

there’s a 50% chance that somebody who

you go back to is going to be willing to

accept your offer anyway, then you should look

at the first 61%, and then use that to set the

standard which you’ll then use for evaluating the remainder. And then if you get to the

very end of this period and haven’t found

anybody, then you go back and make an

offer to the person who was the very best, which

you now know because you’ve explored all of the options. PETER NORVIG: Tom? So if you had prior

knowledge of the distribution that you’re drawing

from, that should also [INAUDIBLE] the period, right? TOM GRIFFITHS: That’s right. So in this case, we’re

assuming that the only way that you can evaluate people is

relative to one another, right? And so that’s

something which then leads to this kind

of strategy, where you have to spend

some time building up an impression of what the

distribution looks like. So basically, pretty

much any variant on this problem

you can imagine has been explored by mathematicians

in the last 50 years. The case that you’re talking

about, where you have what’s called full information–

you actually know what the

distribution is like– is one where the overall strategy

looks quite different. So in that case, what you

should do is set a threshold. And then as you go

through the pool and you’re sort of remaining

candidates become sparser, that threshold becomes

lower and lower. Some of us might

have experienced this in the context of other

kinds of romantic interactions. But it certainly makes

dire predictions, perhaps, as you age and people

start getting married, that you should be willing

to accept, perhaps, a slightly– set a

slightly lower threshold in terms of the way that

you approach the problem. And there are also

variants which are what are called partial

information versions, where you come in not knowing

what the distribution is but having some information about

what that distribution is. And those turn out to

be some of the sort of most interesting and

mathematically intricate cases. So these examples

illustrate some of the ways in

which the secretary problem can be made

more complicated and can accommodate some of

the other kinds of situations that we might encounter in

realistic romantic scenarios. But this is, by all

means, not the limits of optimal stopping in

terms of its implications for human lives. So basically, any

situation where you have to make a decision

about whether to continue to gather information or

to continue to consider opportunities or to

act on the information that you have so

far is going to be one which is going to fit

this same kind of schema of optimal stopping. So another example is deciding

when to sell an asset. So be it your house

or your company, you have to make a

decision in a situation where you might receive

a series of offers. But in this case,

each of those offers is going to cost

you money, right? You’re going to

be waiting around for somebody to come along

and make another offer. And your goal is to

maximize the amount of money that you get out

of those offers. So this can be formulated as

an optimal stopping problem. You have to decide

for each offer whether you’re going

to take that offer. And there’s a

simple formula that describes the strategy

that you should take for solving this problem. So basically, the strategy

takes the general form of a threshold. You should set a

particular value based on your expectations

of the distribution of offers that you’re going to receive. And then the first offer that

exceeds that value should be the one that you accept. This is more closely

analogous to the situation that you were talking about. So, for example, if you have,

say, a uniform distribution between getting an

offer of $400,000 and an offer of $500,000,

then as a function of the cost per offer, we can

actually work out what this threshold looks like. And so it gives you a very

simple kind of approach that you can take in the context

of trying to decide whether you should evaluate an offer. And it also says that you

should never look back, right? So if you turned down

an offer in the past, that was because the offer

was below your threshold. And as a consequence,

you shouldn’t regret having given up

on that opportunity. You should just

be waiting around for the next offer that

exceeds your threshold. Another example of an

optimal stopping problem, which I think many of

us have encountered, is the problem of figuring out

how to find a parking spot. So in this case, the

kind of ideal scenario that the mathematicians

imagine– although, again, there are lots of

variants– is one where you’re driving

towards a destination, and you kind of have a series

of possibly available parking spots that are along

the side of the road. And your goal is to minimize

the distance that you have to end up walking. So it turns out that the

solution to this problem depends on what’s

called the occupancy rate, the proportion

of those parking spots which are occupied. And so for each occupancy

rate, what we can do is identify at what

point you should switch from driving to

being willing to take the next available parking spot. And so we calculate for you

a nice convenient table. You can cut this out,

stick it on your dashboard. But basically, you can get

some interesting conclusions from this, such as if

10% of the parking spots are free– so a 90%

occupancy rate– then you should start looking

for a parking spot seven spaces away

from your destination. Whereas if 1% of those

parking spots are free, then it’s more like 70. And maybe there’s a

scenario down here which fits to some

parts of San Francisco. So another famous problem which

has been analyzed in this way is one which, unfortunately,

ruins the plot of a lot of heist movies. So this is the

problem of a burglar who has to make a

decision about when to give up a life of crime. So there’s a scene that happens

in a lot of heist movies where the team has to sort

of coax the old thief out of retirement. The thief is kind

of going, well, you know, I kind of

like living in my castle and trying to figure out exactly

what they’re going to do. But to sort of spoil all

of those plots, in fact, there’s an exact

solution, and the thief need only crunch the numbers to

work out what should be done. And if you assume that you have

a thief who for each robbery is going to get, on average,

about the same amount of money and has some probability

that they succeed in executing those robberies,

and if they get caught, they lose everything. So the goal is to maximize

the expected amount of money that you end up with,

then the optimal stopping rule is to stop after

a number of robberies equal to the probability

of success divided by the probability of failure. So if you are a ham-fisted

thief who succeeds about half the time and fails

about half the time, you could pull off one robbery. And then you should just quit

if you got away with it away with it and you’ve been lucky. But if you’re a skilled thief

who succeeds 90% of the time and fails 10% of the time, you

can pull off nine robberies, and then that’s the point at

which you should call it quits and go and live in

the castle and not listen to any of these

guys who come calling. So these sorts of scenarios

might seem a little bit artificial, right? They’re all cases where

you’re kind of forced into a situation where you have

to make a decision about when to stop doing something. But I think there’s

a deeper point here, which is that while we normally

think about decision-making as being something

where we’ve got all the information in front

of us, and it’s just a matter of choosing what

we’re going to pursue, in fact, in most

human decisions, we’re in a scenario which

is much more like one of these optimal

stopping problems, where we have to be

gathering information. And one of the decisions

that we have to make is whether we’ve got

enough information to act. And so I think there’s a

deeper point here about the way that we think about the

structure of human decisions, that often we’re engaging in

exactly this kind of process even though we might

not realize it. BRIAN CHRISTIAN:

The second class of problems that we

consider in the book are ones that we describe as

explore/exploit trade-offs. And this encompasses

a wide range of problems where we get to

make a similar kind of decision over and over and over

in an iterated fashion. And typically,

that takes the form of a tension between doing our

favorite things– the things we know and love– or

trying new things. And this type of a

structure appears in a number of different

domains and in everyday life, restaurants being

the obvious case. Do you go to your

favorite place? Or do you try the new

place that just opened up? It happens in music,

where do you do you listen to your favorite album? Or do you put on the radio? It also describes

our social lives. How much time do you spend with

your close circle of friends, your spouse, your family,

your best friends, versus going out to

lunch with that colleague that you just met and you think

you have something in common and want to kind of foster

a new acquaintanceship? This same trade-off

also occurs in a number of different places in more

societal ways– in business and also in medicine. So in business, this

comes up in the context of ads, which I

hear is something that you guys know a little

bit about here at Google. So when you’re deciding what

ad to run next to a keyword, for example, you’ve got

this tension between there is some ad that historically

has the best track record of getting the clicks. But there’s also this

ever-changing dynamic pool of new ads that are

entering the system that might be worth trying. They might be better. They probably aren’t,

but they could be. In medicine, this

structure describes the way that clinical trials work,

where for any condition, there is some known best

treatment with some known chance of success and

some known drawbacks. And then there’s

a series– there’s kind of a pipeline of these

experimental treatments that, again, might be

better, might be worse. And so we have to trade off

between exploring– that is, spending our energy

gathering new information– and exploiting, which is

leveraging the information that we’ve gathered so far

to get a known good outcome. The canonical

explore/exploit problem that appears in the

computer science literature is known as the

multi-armed bandit problem. And this colorful

name– I’m sure this is familiar to

some of you in the room. But the name comes from the

moniker of the one-armed bandit for a slot machine. So a multi-armed bandit you

can think of as just a roomful of different slot machines. So the basic setup

of the formal problem is this– you walk

into a casino. There’s all sorts of different

slot machines, each of which pays off with some probability. But every machine is different. Some of them are more

lucrative than others. But there’s no way for you

to know that until you just start pulling the

levers and seeing which ones seem more promising. So again, here’s

this case where you have to trade off

between gathering information and leveraging

the information that you have. And so there’s this

question, which vexed an entire generation

of mathematicians, of, OK. Let’s say you walk into the

casino, and you have 100 pulls. You’re there for an afternoon. You have enough

time for 100 pulls. What strategy is going to give

you the highest expected payout before you leave the casino? In fact, for much

of the 20th century, this was considered unsolvable. And during World War II, Allied

mathematicians in Britain joked about dropping the

multi-armed bandit problem over Germany as the

ultimate instrument of intellectual

sabotage to just waste the brainpower of the

German scientists. And I think one of the

simplest explanations of the way in which this problem

can be very tricky to think about is the following choice. So let’s say you’ve played

one machine 15 times. And nine times, it paid out. Six times it did not. Another machine

you’ve played twice. Once it paid out. Once it didn’t. Now, if we just want to very

straightforwardly compute the expected value of

each of these machines, the nine-and-six machine’s

got a payout rate of 60%. The one-and-one machine

has a payout rate of 50%. And so there are these two kind

of competing intuitions here. One is, well, you

should obviously just do the thing with

the better expected value. The other is, well, there’s

a sense in which we just don’t know enough about

the second machine to walk away from it forever. Certainly, it must be worth one

more pull or two more pulls. How do you decide what

that threshold is? And it turns out this is,

in a way, a trick question because it all depends on

something that we haven’t given you in this description

of the problem yet, which is how long you

plan to be in the casino. So this is a concept

that sometimes gets referred to as the horizon,

we refer to as the interval. And this concept has,

just speaking personally, given me a bit of

an axe to grind with one of my favorite films

from my own childhood, which is the inspirational 1980s Robin

Williams movie, “Dead Poets Society.” It’s one of these

really feel-good movies, and he plays this

inspiring poetry teacher who says to his students

in this rousing monologue, “Seize the day, boys. Make your lives extraordinary.” And going back through the

lens of the multi-armed bandit problem, I can’t help feeling

that Robin Williams is actually giving two conflicting

pieces of advice here. If we’re just trying

to seize the day, we probably want to pull

that nine-six because it’s got the higher expected value. But if we want to make

our life extraordinary, then we should

certainly see if there isn’t some value in trying

these new things because we can always go back. In standard American English,

we have all of these idioms like “eat, drink, and be

merry, for tomorrow we die.” But it feels that we’re missing

the idioms on the explore side of the equation, which are

things like, life is long, so learn a new language and

reach out to that new colleague because who knows what could

blossom over many years time. We’re still honing

the messaging, but it does feel like there’s

a gap in the culture that can be filled here. So when you’re working

with a finite interval, the solution to the

multi-armed bandit problem comes from a method

described by Richard Bellman, dynamic programming,

where you basically work backwards and are

able to compute the expected value of every

pull given all of the possible pulls that you could make as a

result of whether that succeeds or fails. And you can actually work

out the expected value all the way back to walking in

the door of the casino, what should you do? And this provides

an exact solution to the multi-armed

bandit problem, but there’s a catch, which is

that it requires that you know exactly how long you’re

going to be there and exactly how many

machines there are. And it also requires doing a

lot of computation up front. But I think the

critical thing is that we’re able to look

at these solutions, these exact solutions, and get

some broader principles out of it. So, for example, the

value of exploration is greatest the minute you

walk through the door for two reasons. The first is that if you think

about it in the restaurant analogy, you just

moved to Mountain View. You go out to eat that night. The first place you

try is guaranteed to be the best

restaurant you’ve ever experienced in Mountain View. The next night, you

try a different place. It has a 50% chance

of being the best restaurant you’ve ever

seen in Mountain View, and so on and so forth. So the likelihood

that something new is better than what

we already know about goes down as we gain experience. The second reason

that exploring is more valuable at the

beginning of an interval is that when we

make that discovery, we have more chances to go back. So discovering a really

amazing restaurant on your last night in town is

actually a little bit tragic. It would have been great

to find that sooner. And so this gives us

this general intuition that as we perceive ourselves

to be on some interval of time, we should kind of

front-load our exploration and weight our

exploitation to the end, when we both have the most

experience with what to exploit and the least time remaining

to discover and enjoy something new, even if we did find it. This is significant, I

think, because it gives us a new way of thinking about

the arc of a human lifespan. And so ideas from the

explore/exploit trade-off are now influencing

psychologists and changing the way we think about

both infancy and old age. So to demonstrate

infancy, we have a picture of a baby eating a power cord. And I think this

demonstrates what a lot of us kind of

culturally intuitively think of as the

irrationality of babies. They’re totally– have the

attention span of a goldfish. They put everything

in their mouth. They’re distracted

really easily. They’re really bad at just

generally doing things. We give the example in a

book– like a baby gazelle is expected to be

able to run away from a wolf within the

first day of being alive. But, you know, it

takes us 18 years before we’re allowed

to get behind the wheel of a car, that kind of thing. And the psychologist

Alison Gopnik uses ideas from the explore or

exploit trade-off as a way of saying, well,

maybe this extended period of dependency is actually

optimal in some sense because if you’re in the

casino, for the first 18 years that you’re in the casino,

someone else is buying your food and paying your rent. And so you don’t need to be

getting those early payouts to buy your lunch. And so you can really use that

period of time to explore, which is exactly what

you should be doing at the beginning of your life. There’s a sense in

which just putting every item in the

house in your mouth at least just once

sort of resembles walking into the casino and

just pulling all of the levers. Similarly, the idea

of exploitation is changing the way we

think about getting older. So here we have a gentleman

who I like think of, imagine it as enjoying the same

lunchtime restaurant that he’s been to

hundreds of times. And he knows exactly

what he’s going to get and exactly what he

likes, and it’s great. There’s a lot of

psychological data that says that as

we go through life, older folks have a smaller

circle of social connections. They spend their time

with fewer people. And there’s one interpretation

of this that just says, well, they’re lonely, or they’re

detached or disinterested, or it’s just kind

of sad to get older. But thinking about it from the

perspective of exploitation gives a totally different story. And this comes up in the work of

the Stanford psychologist Laura Carstensen, who studies aging in

an attempt to sort of overturn some of the prejudices we have. And so, for example,

one of the intuitions you get from the idea of the

explore or exploit trade-off is that towards the

end of your life, you really should

be spending more of your time doing the things

you already know and love both because it’s unlikely

to make a discovery that’s better than the things you

already really care about and also because

there’s less time to enjoy it should you do that. And so it just makes more sense

to spend more of your energy on the things that you

already know and love. And so as a result,

what I think is actually a very encouraging story here

is that as you spend more time in the casino, your average

payouts per unit of time should go up. So there’s a sense in

which we should actually expect to get steadily

happier as we go through life. We are less disappointed

and less stressed out. And her research supports this,

which I think is really lovely. Now, there are many cases

where we don’t necessarily know where we are on

the interval of time, or it doesn’t

necessarily make sense to think of there being

some finite interval. So maybe you move

to Mountain View, and you don’t know

how long you’re going to live in Mountain View. Or if you’re a

company, you imagine yourself being interested in

being around indefinitely. But nonetheless,

there’s still a sense in which you care about the

present more than the future. This framing of the problem

led to a different series of breakthroughs, starting

with an Oxford mathematician named John Gittins,

who was hired by the pharmaceutical

company Unilever to tell them, basically,

how much of their money to invest in R&D. And so

he frames the– he almost accidentally made this enormous

breakthrough in the problem by thinking of it

not as there being some finite interval of

time but as there being some indefinite future that

is geometrically discounted. So I don’t know

how long I’m going to be living in the Bay Area. But a really good meal

next week is maybe only 90% as valuable as a really

good meal this week. Or making X dollars

next quarter is only 90% as valuable as making

those dollars this quarter. And it turns out

that, again, you can get a very precise

solution to this problem. So he explored it in

this business context. But it’s also, I think,

very interesting that it was a pharmaceutical context,

because this also gives us a way of thinking

differently about how a clinical trial should be run. The basic idea behind

Gittins’s breakthrough here, which is called

the Gittins index, is he imagines that– the

word we use is a bribe. So if you think about– there’s

a game show that is on TV called “Deal or No

Deal,” where you have a briefcase that

has somewhere between one and a million dollars in it. And someone calls you

on the phone and says, I will pay you $10,000 not

to open that briefcase. What do you do? This is the basic intuition

behind the Gittins index. So Gittins says,

for every machine that we’ve tried and have

incomplete knowledge of– or maybe we have no

knowledge of whatsoever– there’s some machine with

a guaranteed payout that’s so good, we’ll never try

that machine ever again. Maybe the nine-six versus the

one-one is more of a toss-up. But if it was 9-0

and the one-one, then there’s a sense

in which maybe it’s just never worth pulling the

one-one machine ever again. And so Gittins comes

up with what he thinks is a nice approximation,

which is just always play the machine with

the highest bribe price. And to his own astonishment,

as well as the field’s, this turns out to be, in fact, not

merely a good approximation but the solution. So this is another case where,

like with the parking problem, we present this

table in the book, and you can cut it out

and take it home with you. And it provides

values for situations where you’re trying to

weigh the value between two different options. And so going back to our

two slot machines, the nine and six machine has a

Gittins index of 6,300. But the one-and-one machine

has a Gittins index of 6,346. So case closed. Pull the one-one

machine one more time. What I think is kind of

philosophically significant about this is the

zero-zero square has a value of 70.29%, which

means that you should consider something you’ve never tried as

being just as good as something that you know works

70% of the time, even though it only has

an expected value of 50%. And you can see if you follow

the diagonal down to the right, it goes from 70% to

63.46% to 60.10%, 58.09%. And it does indeed converge

on 0.5 as you gain experience. But there’s this boost applied

for not having that experience. So we tongue-in-cheek suggest

that you just print this out and just use it to

decide where to eat. But there are

sometimes some problems that come up with this. One is that we don’t always

geometrically discount our payoffs. The other is that

actually computing these values on the fly is kind

of computationally intensive. And so there’s a third way of

thinking about the problem that has come in the wake

of Gittins’s work, and that is the idea

of minimizing regret. So we give a lot of

examples that touch on Google’s work, but the

best illustration of this actually comes from Amazon. So Jeff Bezos talks about being

in this really lucrative hedge fund position and deciding

whether to give up his cushy job to start

an online bookstore. And he approaches it from what

he calls a regret minimization framework. “I knew looking back

I wouldn’t regret it.” In the context of the

multi-armed bandit problem, you can formulate

regret as every time you tried something that wasn’t

the best thing in hindsight. And so you can ask yourself,

how does my regret– what does that look like as I proceed

through my time in the casino? And we have good

news and bad news. We’ll start with the bad news. The bad news is that you will

never stop getting more regrets as you go through life. The good news is that the rate

at which you add new regrets goes down over time. Specifically, if you were

following an optimal algorithm, the rate at which

you add new regrets is logarithmic with

respect to time. And this has led to a series

of breakthroughs in computer scientists looking for simpler

solutions than the Gittins index that still have this

optimality of minimal regret. One of our favorites, which

I think is the most thematic, is called upper

confidence bound. And this says that for every

slot machine– you know, you’ve got some error

bars around what you think the payoff might be. So the expected value would be

in the middle of that range. But there’s some error bars

on either side of that. Upper confidence

bound says, simply, always do the thing with the

highest top of the range. Don’t care about the

actual expected value, and don’t care about

the worst case scenario. Just always do the thing with

the highest top of the range. And I think that’s sort

of a lovely, lyrical note that the math brings us to,

which is that optimism is the best prevention for regret. TOM GRIFFITHS: So

our third example begins in a different place,

which is in the closet. So I think all of us have

encountered a problem of an overflowing closet. Things need to be

organized, but you also need to make a

decision about what you’re going to get rid of. And in order to

solve this problem, we’d like to be able

to turn to experts. Fortunately, there are experts

on exactly this kind of thing. So we could consult one of

these– Martha Stewart, who says to ask yourself a

series of questions– how long have I had it? Does it still function? Is it a duplicate of

something I already own? And when was the last

time I wore it or used it? And then based on the

answers to these questions, you can make a decision

about whether you should keep that thing or not,

give it away to charity, and, as a consequence, end up

with a more organized closet. So there are a couple of

interesting observations here. The first is that here there

are in fact, multiple questions that you should be answering. And the answers

to these questions could be quite different. And the other is

that, in fact, there’s another group of experts who

have thought about exactly these problems and come up

with slightly different advice. In particular, they discovered

that one of these questions is, in fact, far better

than any of the others. So this other group of experts

don’t think about closets. They think about the

memory of computers. This is the picture of

the Atlas computer, which was a computer which

was built at Manchester University in the 1960s. And Atlas had an

interesting structure, where it had two kinds of memory. It had a drum which could

store information in a way where it was very

slow to access. And then it also

had a set of sort of magnets which could be

used to store information in a format which was

relatively fast to access. And when they first

built the machine, the way that they were using it

was to read off the information would be needed for a

computation from the drum, and then store it in

the magnetic memory, and then do the operations, and

then write it back to the drum, and then take the next

part of the computation and read off all of the relevant

information from the drum, and then do the operations,

then write it back to the drum. But a mathematician who

was working on Atlas named Maurice Wilkes realized

that there was a better way to solve this problem. He realized that they

could make the whole system work much faster if

they didn’t always take all of the information

out of the fast memory and put it back into

the slow memory, but rather they kept around

the pieces of information which they thought

they were going to need to use again in the future. So the reason why

this speeds things up is that then you

don’t have to spend the extra time reading

those things back off the slow memory. And as a consequence, the

computer runs much faster. So this is an idea which

computer scientists now recognize as caching. So it’s the idea of keeping

the information which you’re most likely to need in the

future in the part of memory which is most easily and

most rapidly accessed. But it brings with

it another kind of algorithmic problem, which

is the problem of figuring out exactly what those

items that you’re likely to need in the future

are going to be or, to put it another way, what it is

that you should throw away. And this is a

problem that’s called the problem of cache eviction. So cache eviction

is something which requires us coming up

with good algorithms for deciding what

we’re not going to need again in the future. And the person who really

made the first breakthrough in thinking about this is

this man, Laszlo Belady, who was working at IBM. So before he worked at IBM,

Belady had grown up in Hungary, and then fled during

the revolution there with only a bag containing

one change of underpants and his thesis paper. And then he ended up

having to then emigrate from Germany, which is

where he moved to, again with very minimal equipment. He just had $100 and his wife. So by the time he’d

reached IBM in the 1960s, he’d built up a

significant amount of experience in deciding

what it was that it made sense to leave behind. So Belady described

the optimal algorithm for solving the problem

of deciding what you should evict from your cache. And this optimal algorithm

is essentially clairvoyance. What you should do is evict

from the cache that piece of information which

you are going to need the furthest into the future. So as long as you can

see into the future as far as you need to go in

order to make that decision, then you can solve this problem. You can sort of do the

best possible solution to this problem that

you can imagine. Unfortunately,

when engineers have tried to implement

this algorithm, they’ve run into problems. And so for mere mortals, we need

to have some different kinds of algorithms. And Belady actually evaluated

three different kinds of algorithms– one where

you just randomly evict items from the cache, one where the

things which were first entered into the cache are the

ones which first leave it, and one where you evict

those things which are least recently used. That is, those items which have

been used the furthest distance into the past are the ones

which leave the cache first. And doing an

empirical evaluation of these different

schemes, he discovered that there was one clear winner,

which is the least recently used algorithm. So basically, the idea

is that the information that you used least

recently is least likely to be the

information which you’re going to need again in the

future as a consequence of a principle that

computer scientists call temporal locality– basically

that if you just touched a piece of information, you’re

going to be likely to need that information again

in the near future because there’s a kind

of correlation over time in the pieces of information

which an algorithm might need to access. So taking this insight, you

can build caching systems which work very

efficiently in a variety of different situations. So nowadays, caches are

used all over the place. So if we look on

computers, we find that you’ll see multiple chips

that are dedicated to caching. There are caches that are

built into hard disks. There are other

kinds of caches which are used in servers

for delivering websites to people as quickly and

efficiently as possible. But the one place where these

caching algorithms perhaps haven’t been applied and perhaps

should is back in our closet. And if we look at these

ideas that Martha provides us with how to organize

our possessions, then as we go through

these possibilities, it’s clear that

one of them might be a better recommendation

than the others, which is when was the last time

I wore it or used it, which is actually an

instantiation of the least recently used principle. So next time you’re

thinking about trying to organize your closet,

it might be worth keeping this in mind, that as

long as your possessions obey the same kind of principle

of temporal locality, focusing on those possessions

that were least recently used might be the most

predictive of those things that you’re least likely to

need again in the future. So this kind of principle

isn’t just something which is useful in

thinking about how to organize your closet. It’s also something

that might be useful in thinking about

how to organize your office. And this was a discovery that

was made somewhat accidentally by a Japanese economist

called Yukio Noguchi. Co Noguchi is a tax economist. He was constantly

receiving reports and papers and documents

that needed to be filed away. And he was kind of overwhelmed

with all of this information. He didn’t have time

to file it properly, so he came up with

a simple solution, which was just to put all

of those papers into a box. But he didn’t just

dump them into a box. What he did was

actually put them into a box in a

very orderly way. So basically, he had a box

which was sort of horizontally aligned. And he put the information into

the box at one end of the box. So as he’d get some

new papers, he’d put those papers in

at the left-hand side. And as a consequence,

you know, the papers would sort of move down the

box as new things came in. And then he did

something else important, which is that as he used

one of those papers, he’d pull it out of the box. And then when he was

finished using it, he’d put it back in again at

the left-hand side of the box. So this has a clear connection

to least recently used caching, right? Once your box fills up, you

need to get rid of something. And you can get rid

of the things that hit the right end of

the box because those are the things which you

used furthest in the past and consequently, least likely

to need in the near future. But this principle

of taking out a file and then putting it back at

the left-hand side of the box also corresponds to

another idea which has shown up in theoretical

computer science. So we can actually show

that this way of organizing his information

is something which is near optimal, or

at least as close to optimal as we’re

likely to be able to get. So the actual data structure

that he had created here is something that a computer

scientist would recognize as a self-organizing list. So basically, in a

self-organizing list, you have a sequence of

pieces of information. And then as you access

those pieces of information, you have the opportunity

to change the order that those pieces of

information appear in. And so this idea of taking the

information that’s accessed and then putting it at the

very front of the list, or at the left-hand

side of Noguchi’s box, is actually something

which turns out to be a very

effective algorithm. So Robert [? Tagin ?]

and Daniel Slater proved in 1985 that moving

the most recent item to the front of the list

is, at worst, twice as bad as clairvoyance. So clairvoyance is the best

that you could possibly do. And it turns out, this

is the only algorithm that comes with a

theoretical guarantee of being at least

close to clairvoyance in multiplicative terms. So if you’re thinking about

implementing the Noguchi filing system in your

office, it might be reassuring to realize that

perhaps you already have. So we normally think

about a messy office as being a bad thing. And in particular, a

giant pile of papers on your desk like

this is something which kind of seems like a

poor method of organizing information. But you can kind

of think about this as taking the Noguchi system,

and then literally turning it on its side. Right? So a big pile of papers is, in

fact, a self-organizing list. And if you’re taking

things out of the pile and then sticking

them back on the top and putting the most

recently used items on the top of the

pile, then you’re implementing exactly this

relatively optimal strategy for organizing the information

that’s contained in that list. So if you’re somebody who

is familiar with these kinds of messes, you’ll

also be reassured by some of the message in

our sorting chapter, where we argue against sorting in

many domestic situations. Thinking about

caching isn’t just useful for thinking about

how to organize information around you. It’s also something which might

give you new insights into how human memory works. So I think there’s an

intuition that a lot of us would have about

memory, which is kind of thinking

about it as something sort of like Noguchi’s box. Right? You’ve got kind of a limited

amount of space in your memory. And so when you

learn something new, you have to put it in there. And when you do that, maybe

it pops something else out. And as a consequence,

you forget that thing. And so forgetting is

just a consequence of kind of hitting a

capacity limit in terms of the amount of information

that we can store. But a cognitive scientist called

John Anderson has actually proposed that there’s a

different way of thinking about how memory works and

thinking that the analogy is less like a box of finite

size and more like a library of infinite size. So if you have a library which

has infinitely many books arrayed along a sort of

linear shelf like this, then the problem

that you have is one not of figuring out

where to fit information but rather one of figuring out

how to organize information. Another good analog of this

is thinking about something like web search, where you’ve

got a whole lot of web pages, and you want to organize

those web pages in such a way that you can find the

things that people are likely to be looking for

with high probability close to the top of the

list that you produce. So from this perspective,

forgetting something isn’t that you’ve sort of

had that thing sort of pop out of your memory but

rather that the time it would take you to find

that thing is greater than the amount of time that

you’re willing to spend, that the way that

information is organized is not sufficiently

good to allow you to identify that item quickly. And so this makes an

interesting prediction, which is that we

should be trying to organize those

items in memory such that the things that we

think we’re most likely to need in the future are going

to be the things which we find easiest to recall. And Anderson actually showed

some evidence for this. So he took some famous data. This is data from

an experiment which was done in the 19th century

by an early psychologist, Ebbinghaus, who

basically taught himself some lists of

nonsense syllables, and then would look at how well

he could recall those lists some number of hours

after he’d memorized them. And so what Anderson

did was look at whether this pattern of

recall, where, basically, you get this kind of rapid

falloff followed by a slow, sort of long tail

could be predicted by looking at how

likely it is that we’re going to encounter particular

pieces of information in our environment. And so what he did was go

to the “New York Times,” look at headlines in

the “New York Times,” and then look at how

likely a word was to appear in the headline

in the “New York Times” as a function of how

long ago it previously appeared in those headlines. So he could look at the

relationship between the number of days that had elapsed,

and then the probability of an item appearing. And he found that this showed

a very similar kind of curve. So this kind of correspondence

between the probability that something is

likely to be needed as a function of how

long ago it was used and the patterns of recall

that we see in human memory provides one suggestive

form of evidence, that one of the things

that our minds are doing is trying to organize

information in such a way that we are keeping

around those things that we are likely to

need again in the future. BRIAN CHRISTIAN:

Thinking computationally about the types of problems that

we encounter in everyday life has payoffs at a number

of different scales. The overarching

argument of the book is there are deep parallels

between the problems that we face in our lives and the

ones that are considered some of the fundamental and canonical

problems in mathematics and computer science. And this is significant

because as a result, there are these simple,

optimal strategies that are directly relevant to those

domains in our own lives. And there’s something

very concrete that we can use and learn from. And even if we’re not literally

going to stop at exactly, you know, 37% or so

forth, having a vocabulary and knowing what

an optimal stopping or an explore or exploit

problem looks like and having a general sense

of how the solution is structured gives us a way to

bolster our own intuitions when we find ourselves

in those situations. And I think most broadly,

a lot of the solutions that we explore

don’t necessarily look like what we think of when

we think of what computers do, which gives us an opportunity

to actually rethink our notion of

rationality itself. So intuitively, we kind of have

this bias that being rational means being exhaustive, exact,

deterministic, considering everything, getting

an exact answer that’s correct 100% of the time. In fact, this is

not what computers do when they’re up against the

hardest classes of problems. This is kind of the

luxury of an easy problem. And up against an

intractable problem, computer scientists turn

to a totally different set of techniques. When we take into account the

cost, the labor of thought itself, the best strategies may

not be to consider everything, to think indefinitely, to

always get the right answer in each situation. We may want to, in fact,

trade off the labor of the computation versus

the quality of the result. And as the book progresses,

especially in the second half, we look at what

these strategies are for dealing with

intractable problems, which most of the ones that we

face in real life are. And that leads to

this conclusion, that what computer

scientists do up against the hardest

classes of problems is they use approximations. They trade off

the costs of error against the costs of delay. They relax some of the

constraints of the problem, and they turn to chance. These aren’t the

concessions that we make when we can’t be rational. These are what being

rational means. We explore this line of

thinking through a number of different domains. We’ve talked about three today. We also look at

sorting algorithms– what do they tell you about

how to arrange your bookshelf and, more importantly,

whether you should? We look at scheduling theory. Every operating

system has a scheduler that tells the CPU what to

be doing when, for how long, and what to do next. So we look at what the

parallels are there for thinking about time

management in our own lives. And in the context

of Bayes’s rule, we think about problems of

predicting the future– how long a process will go on, how

much money something will make based on what it’s made so far. And, on a personal

level, you’ve been dating someone for a couple months. It’s going pretty well so far. Is it premature to

book that weekend place in Tahoe at the

end of the summer? What should you do? And we provide some rational

answers there, as well. And unlike the types

of advice that you might find in, for

example, self-help books, the insights that are derived

from thinking computationally about these problems

are backed by proofs. Thank you so much. [APPLAUSE] BORIS DEBIC: Questions? BRIAN CHRISTIAN: Do you want

to get more in the light? Yeah. AUDIENCE: So how useful is it to

have a proof of an abstraction when the real life doesn’t

match the abstraction? TOM GRIFFITHS: Yeah. So I think the

way that we really think about this is

there are definitely simplifications that go into

formulating these problems. But what you get out

of them is if you’re in exactly that

situation, you know exactly what you should do. But more generally,

you get insights about how those solutions change

as a consequence of changing the assumptions. So, for example, I talked

about some of the variants on the secretary problem. And from that, you might

not know exactly what the number is in your scenario. But you can recognize, OK. Well, if it becomes

more permissive, then I should be more

willing to spend longer looking before I start leaping. And if it becomes

less permissive, than I should have a much

more rapid transition from those things. And I think there’s a

related question here, which is if we think that

people should follow algorithms, why don’t we just

make computers that will solve these

problems for people, and then people don’t have

to make any decisions at all? And I think one of

the things that people are really good

at is figuring out how to interpolate between

these possibilities and how to kind of evaluate

some of the fuzziness around the particular

problems that we’re facing. And so we’re really

providing tools that can guide those

human capacities in terms of thinking about solutions

to more realistic problems. AUDIENCE: Very

interesting topic. How long it take you

guys to write this book? BRIAN CHRISTIAN:

There’s a quote that we use at the beginning

of the book, of the chapter on scheduling. We have, the

epigraph says– it’s from Eugene Lawler, who was

a researcher in scheduling theory. And he says, “why don’t we write

a book on scheduling theory, I asked. It shouldn’t take much time. Book writing, like

warmaking, often entails grave miscalculations. 15 years later, scheduling

is still unfinished.” So I think Tom and I had

an analogous experience, where we– I think of the book

as really emerging in a dinner that Tom and I had in

2011, where we– I mean, we’ve known each

other for 11 years. These are shared

obsessions that we’ve talked about for a long time. But we basically

realized that we wanted to write the same book,

what amounted to the same book. And so that was when we decided

to team up and work together. And we had what in hindsight

was a sort of predictably naive sense of like,

oh, it should take about 18 months or something. It’ll be out in 2013. So here we are. And you can tell how

that plan worked out. TOM GRIFFITHS: I

should also point out another terrible

thing that can happen to a book is having

a small child. So my wife and I

had our second child somewhere in that process,

which threw everything off. AUDIENCE: Are there any

rejected chapters in this book? Are there any

areas of life where you looked hard for an analog,

and it didn’t work out? TOM GRIFFITHS: Yeah,

that’s interesting. So our rejected

chapters are more that there are lots and

lots of algorithmic ideas that we would love

to write about, but we just ran out of

space and time to include. So we’ve actually

got a folder which is called Sequel, which

is the only way that we were happy cutting things,

so we could pretend. And so that contains a bunch

of chapters and proto-chapters that explored a lot of

different kinds of algorithms. And in some cases, it was

that there’s algorithms that have already got good press. And in other cases,

it was that we really felt like there was a key

insight that those things could give you about human lives. But either you had to get

too far into the weeds in order to get out what that

insight was or it was something where– like, basically,

the examples we give in the book have been

sort of carefully selected for exactly

the right blend of you need to understand a

certain amount of math in order to get a

practical payoff. And some things just didn’t

reach that threshold. BRIAN CHRISTIAN: We

also had a beta version of a chapter on data structures

that had a lot of great stuff that we still kind of

wish we could have saved. But it just didn’t fit under

the rubric of the book. So that, I guess, lives in

the Sequel folder now, too. AUDIENCE: Do you feel

like you learned anything about the limits or lack thereof

of what machine intelligences could be capable of? It seems like a lot

of these examples right now involve pretty

specific parameters for what the problem has to be,

but also that there’s just a ton of similarity between

how humans actually do things and how computers

end up doing them. BRIAN CHRISTIAN:

This is one where I think Tom can speak as a

machine learning researcher. But I would just

say, as a preamble, I think exactly how

you’ve formulated the question is how

I think of it, which is that a lot of the

algorithms that we discuss involve assumptions about

the distribution of values. The Gittins index, the

way that we present it, assumes a uniform distribution,

or the house-selling problem assumes uniform distribution. And often, the hardest

versions of these problems are what are called partial

information problems, where you have to

be making inferences about what you think

the distribution looks like on the fly based on the

values that you’ve encountered. And those often turn out to

be the intractable problems. And so there is a sense in which

human intelligence involves making all of these

inferential leaps, but also deciding

how to parameterize the problem in the first place. AUDIENCE: Yeah. I think this also relates

to Peter’s question. So I think as you get closer

to the actual problems that human beings solve,

you sort of start to hit the edges of the theory. Another good example of this

is in the explore or exploit setting, where– so if you

get people and put them in an explore or

exploit scenario, you find pretty consistently

that people deviate from the predictions

that come out of these sort of standard

multi-armed bandit models. And they deviate in a

particular direction, which is that they

tend to over-explore. So kind of at the point where

the algorithm is committed and said, hey, just

keep on pulling that one lever, people

are still like, well, I’m going to go try that one. I’m going to try that one. I’m going to try that

one, and still trying out different options. And so that looks

mysterious until you realize that it’s not the

people are being irrational. It’s that, in fact, the

assumptions of the model are kind of wrong for

a real human situation. So the assumption is that

a slot machine pays off with the same probability. That’s sort of fixed over time. Whereas in a human environment,

the payoff probabilities for different options are

things that change over time. Right? So they might be sort of

slowly drifting around. A particular restaurant is

getting better or worse, or a chef has changed, or

it’s under new management, or– all of those

things are things that over time mean that those

probabilities can be different. And so if you’re in a

situation like that, then what you should

be doing is, in fact, exploring more because you

need to go back and check on the information that you had. But that problem is what’s

called a restless bandit problem, and it’s one

which still presents a challenge for developing

sort of good machine learning methods that can deal with it. So I think there’s plenty

of room to take inspiration from human cognition, as well as

room for making recommendations about humankind. BORIS DEBIC: And with

that, let’s please thank Tom and Michael

for coming to Google. BRIAN CHRISTIAN:

Thank you so much.

First

Algorithm

1. Watch youtube

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Can this be classified as a religion? Or can religion be classified as an algorithm? This book seems like a very individual-focused religion in that case…

First, grown men must NOT wear t-shirts!!!!!

How can you calculate the probability of being caught as a robber if your probability of getting caught is going to be 0 until you're caught? For example, if you have 3 successful robberies, then by looking at previous outcomes (3 out of 3 robberies being successful), you'll conclude that the probability of a successful robbery is 1.0 or 100%.

One problem with implementing Optimal stopping in real might probably be, it is not worth it go to the extent of 37% in terms of time and effort for the payoff of that particular problem.. and it is worth it in some other problems to go beyond because of it's payoff.. or I haven't understood the underlying mathematical structure properly..

Emma is the best! Thanks for such an inspiring talk!

This has given me a lot of ideas, thank you. ðŸ™‚

I am wondering about how I could use these algorithms to be most efficient and accurate when evaluating students essay on English literature.

These Talks at Google are becoming; "what way can we solve the San Francisco housing crisis today?"

I'm shocked. This is fucking genius.

Algorithm:

1. Create boring presentation on algorithms.

nice presentation guys

can you do an algorithm on where ISIS would attack next in Europe so I know which train station to avoid ??

40:00 What about FOMO, or fear of missing out, where instead of dwelling on missed (unseized) opportunities in the past, you dwell on missed (unevaluated) opportunities in the future?

With the cost to "play the slot machine," or message another potential date online, growing ever smaller in today's more connected society, FOMO seems to be on the rise.

Susceptibility to regret versus FOMO likely varies person to person depending on wide ranging factors like prior luck, patience, faith in the system, and your personal utility function (i.e. is it best-or-nothing for you, or would you be just as happy with any outcome above a threshold value). I know that I personally am more prone to regret than FOMO, so like Bezos, this is what I tend to minimize for, but the same may not necessarily be good advice for others.

Interesting waiting is good

booaring, only useful for the unfitted for life

I love geeks. Good luck to you.

It's surprising to find a so-called scientist getting the theory of Optimal Stopping so fundamentally wrong. At about 6 minutes in he says that optimal stopping suggests spending 37% of your time looking for candidates is the best way to find candidates. What the theory actually says is if you interview n divided by e candidates then select the next one that is better than all those you've interviewed so far, you'll pick the best candidate on 37% of occasions. Where n is the total number of candidates and e is the base of the natural logarithm. Not nearly the same thing as "spending 37% of your time."

TL;DR: The time spent is variable. The percentage success (37%) is what is constant.

Friend, Front end "exploration" / Back end "exploitation", seems to describe Mormon Batch Dating & single / drawn out Victorian Courting. In both cases presumably without sex.

Please!!!

Can anyone summerize video?

Video good or bad?

He looks like Bill Clinton though

So hard pill to swallow!!!

do it out of body http://www.outofbodyjournal.com