Lex Fridman Podcast - #12 - Tuomas Sandholm: Poker and Game Theory

The following is a conversation with Thomas Sanholm.

He’s a professor at CMU and co creator of Labratus,

which is the first AI system to beat top human players

in the game of Heads Up No Limit Texas Holdem.

He has published over 450 papers

on game theory and machine learning,

including a best paper in 2017 at NIPS,

now renamed to Newrips,

which is where I caught up with him for this conversation.

His research and companies have had wide reaching impact

in the real world,

especially because he and his group

not only propose new ideas,

but also build systems to prove that these ideas work

in the real world.

This conversation is part of the MIT course

on artificial general intelligence

and the artificial intelligence podcast.

If you enjoy it, subscribe on YouTube, iTunes,

or simply connect with me on Twitter

at Lex Friedman, spelled F R I D.

And now here’s my conversation with Thomas Sanholm.

Can you describe at the high level

the game of poker, Texas Holdem, Heads Up Texas Holdem

for people who might not be familiar with this card game?

Yeah, happy to.

So Heads Up No Limit Texas Holdem

has really emerged in the AI community

as a main benchmark for testing these

application independent algorithms

for imperfect information game solving.

And this is a game that’s actually played by humans.

You don’t see that much on TV or casinos

because well, for various reasons,

but you do see it in some expert level casinos

and you see it in the best poker movies of all time.

It’s actually an event in the World Series of Poker,

but mostly it’s played online

and typically for pretty big sums of money.

And this is a game that usually only experts play.

So if you go to your home game on a Friday night,

it probably is not gonna be Heads Up No Limit Texas Holdem.

It might be No Limit Texas Holdem in some cases,

but typically for a big group and it’s not as competitive.

While Heads Up means it’s two players.

So it’s really like me against you.

Am I better or are you better?

Much like chess or go in that sense,

but an imperfect information game,

which makes it much harder because I have to deal

with issues of you knowing things that I don’t know

and I know things that you don’t know

instead of pieces being nicely laid on the board

for both of us to see.

So in Texas Holdem, there’s two cards

that you only see that belong to you.

Yeah. And there is,

they gradually lay out some cards

that add up overall to five cards that everybody can see.

Yeah. So the imperfect nature

of the information is the two cards

that you’re holding in your hand.

Up front, yeah.

So as you said, you first get two cards

in private each and then there’s a betting round.

Then you get three cards in public on the table.

Then there’s a betting round.

Then you get the fourth card in public on the table.

There’s a betting round.

Then you get the 5th card on the table.

There’s a betting round.

So there’s a total of four betting rounds

and four tranches of information revelation if you will.

The only the first tranche is private

and then it’s public from there.

And this is probably by far the most popular game in AI

and just the general public

in terms of imperfect information.

So that’s probably the most popular spectator game

to watch, right?

So, which is why it’s a super exciting game to tackle.

So it’s on the order of chess, I would say,

in terms of popularity, in terms of AI setting it

as the bar of what is intelligence.

So in 2017, Labratus, how do you pronounce it?


Labratus beats.

A little Latin there.

A little bit of Latin.

Labratus beats a few, four expert human players.

Can you describe that event?

What you learned from it?

What was it like?

What was the process in general

for people who have not read the papers and the study?

Yeah, so the event was that we invited

four of the top 10 players,

with these specialist players in Heads Up No Limit,

Texas Holden, which is very important

because this game is actually quite different

than the multiplayer version.

We brought them in to Pittsburgh

to play at the Reverse Casino for 20 days.

We wanted to get 120,000 hands in

because we wanted to get statistical significance.

So it’s a lot of hands for humans to play,

even for these top pros who play fairly quickly normally.

So we couldn’t just have one of them play so many hands.

20 days, they were playing basically morning to evening.

And I raised 200,000 as a little incentive for them to play.

And the setting was so that they didn’t all get 50,000.

We actually paid them out

based on how they did against the AI each.

So they had an incentive to play as hard as they could,

whether they’re way ahead or way behind

or right at the mark of beating the AI.

And you don’t make any money, unfortunately.

Right, no, we can’t make any money.

So originally, a couple of years earlier,

I actually explored whether we could actually play for money

because that would be, of course, interesting as well,

to play against the top people for money.

But the Pennsylvania Gaming Board said no, so we couldn’t.

So this is much like an exhibit,

like for a musician or a boxer or something like that.

Nevertheless, they were keeping track of the money

and brought us close to $2 million, I think.

So if it was for real money, if you were able to earn money,

that was a quite impressive and inspiring achievement.

Just a few details, what were the players looking at?

Were they behind a computer?

What was the interface like?

Yes, they were playing much like they normally do.

These top players, when they play this game,

they play mostly online.

So they’re used to playing through a UI.

And they did the same thing here.

So there was this layout.

You could imagine there’s a table on a screen.

There’s the human sitting there,

and then there’s the AI sitting there.

And the screen shows everything that’s happening.

The cards coming out and shows the bets being made.

And we also had the betting history for the human.

So if the human forgot what had happened in the hand so far,

they could actually reference back and so forth.

Is there a reason they were given access

to the betting history for?

Well, we just, it didn’t really matter.

They wouldn’t have forgotten anyway.

These are top quality people.

But we just wanted to put out there

so it’s not a question of the human forgetting

and the AI somehow trying to get advantage

of better memory.

So what was that like?

I mean, that was an incredible accomplishment.

So what did it feel like before the event?

Did you have doubt, hope?

Where was your confidence at?

Yeah, that’s great.

So great question.

So 18 months earlier, I had organized a similar brains

versus AI competition with a previous AI called Cloudyco

and we couldn’t beat the humans.

So this time around, it was only 18 months later.

And I knew that this new AI, Libratus, was way stronger,

but it’s hard to say how you’ll do against the top humans

before you try.

So I thought we had about a 50, 50 shot.

And the international betting sites put us

as a four to one or five to one underdog.

So it’s kind of interesting that people really believe

in people and over AI, not just people.

People don’t just over believe in themselves,

but they have overconfidence in other people as well

compared to the performance of AI.

And yeah, so we were a four to one or five to one underdog.

And even after three days of beating the humans in a row,

we were still 50, 50 on the international betting sites.

Do you think there’s something special and magical

about poker and the way people think about it,

in the sense you have,

I mean, even in chess, there’s no Hollywood movies.

Poker is the star of many movies.

And there’s this feeling that certain human facial

expressions and body language, eye movement,

all these tells are critical to poker.

Like you can look into somebody’s soul

and understand their betting strategy and so on.

So that’s probably why, possibly,

do you think that is why people have a confidence

that humans will outperform?

Because AI systems cannot, in this construct,

perceive these kinds of tells.

They’re only looking at betting patterns

and nothing else, betting patterns and statistics.

So what’s more important to you

if you step back on human players, human versus human?

What’s the role of these tells,

of these ideas that we romanticize?

Yeah, so I’ll split it into two parts.

So one is why do humans trust humans more than AI

and have overconfidence in humans?

I think that’s not really related to the tell question.

It’s just that they’ve seen these top players,

how good they are, and they’re really fantastic.

So it’s just hard to believe that an AI could beat them.

So I think that’s where that comes from.

And that’s actually maybe a more general lesson about AI.

That until you’ve seen it overperform a human,

it’s hard to believe that it could.

But then the tells, a lot of these top players,

they’re so good at hiding tells

that among the top players,

it’s actually not really worth it

for them to invest a lot of effort

trying to find tells in each other

because they’re so good at hiding them.

So yes, at the kind of Friday evening game,

tells are gonna be a huge thing.

You can read other people.

And if you’re a good reader,

you’ll read them like an open book.

But at the top levels of poker now,

the tells become a much smaller and smaller aspect

of the game as you go to the top levels.

The amount of strategies, the amount of possible actions

is very large, 10 to the power of 100 plus.

So there has to be some, I’ve read a few of the papers

related, it has to form some abstractions

of various hands and actions.

So what kind of abstractions are effective

for the game of poker?

Yeah, so you’re exactly right.

So when you go from a game tree that’s 10 to the 161,

especially in an imperfect information game,

it’s way too large to solve directly,

even with our fastest equilibrium finding algorithms.

So you wanna abstract it first.

And abstraction in games is much trickier

than abstraction in MDPs or other single agent settings.

Because you have these abstraction pathologies

that if I have a finer grained abstraction,

the strategy that I can get from that for the real game

might actually be worse than the strategy

I can get from the coarse grained abstraction.

So you have to be very careful.

Now the kinds of abstractions, just to zoom out,

we’re talking about, there’s the hands abstractions

and then there’s betting strategies.

Yeah, betting actions, yeah.

Baiting actions.

So there’s information abstraction,

don’t talk about general games, information abstraction,

which is the abstraction of what chance does.

And this would be the cards in the case of poker.

And then there’s action abstraction,

which is abstracting the actions of the actual players,

which would be bets in the case of poker.

Yourself and the other players?

Yes, yourself and other players.

And for information abstraction,

we were completely automated.

So these are algorithms,

but they do what we call potential aware abstraction,

where we don’t just look at the value of the hand,

but also how it might materialize

into good or bad hands over time.

And it’s a certain kind of bottom up process

with integer programming there and clustering

and various aspects, how do you build this abstraction?

And then in the action abstraction,

there it’s largely based on how humans and other AIs

have played this game in the past.

But in the beginning,

we actually used an automated action abstraction technology,

which is provably convergent

that it finds the optimal combination of bet sizes,

but it’s not very scalable.

So we couldn’t use it for the whole game,

but we use it for the first couple of betting actions.

So what’s more important, the strength of the hand,

so the information abstraction or the how you play them,

the actions, does it, you know,

the romanticized notion again,

is that it doesn’t matter what hands you have,

that the actions, the betting may be the way you win

no matter what hands you have.

Yeah, so that’s why you have to play a lot of hands

so that the role of luck gets smaller.

So you could otherwise get lucky and get some good hands

and then you’re gonna win the match.

Even with thousands of hands, you can get lucky

because there’s so much variance

in No Limit Texas Holden because if we both go all in,

it’s a huge stack of variance, so there are these

massive swings in No Limit Texas Holden.

So that’s why you have to play not just thousands,

but over 100,000 hands to get statistical significance.

So let me ask another way this question.

If you didn’t even look at your hands,

but they didn’t know that, the opponents didn’t know that,

how well would you be able to do?

Oh, that’s a good question.

There’s actually, I heard this story

that there’s this Norwegian female poker player

called Annette Oberstad who’s actually won a tournament

by doing exactly that, but that would be extremely rare.

So you cannot really play well that way.

Okay, so the hands do have some role to play, okay.

So Labradus does not use, as far as I understand,

they use learning methods, deep learning.

Is there room for learning in,

there’s no reason why Labradus doesn’t combine

with an AlphaGo type approach for estimating

the quality for function estimator.

What are your thoughts on this,

maybe as compared to another algorithm

which I’m not that familiar with, DeepStack,

the engine that does use deep learning,

that it’s unclear how well it does,

but nevertheless uses deep learning.

So what are your thoughts about learning methods

to aid in the way that Labradus plays in the game of poker?

Yeah, so as you said,

Labradus did not use learning methods

and played very well without them.

Since then, we have actually, actually here,

we have a couple of papers on things

that do use learning techniques.


And deep learning in particular.

And sort of the way you’re talking about

where it’s learning an evaluation function,

but in imperfect information games,

unlike let’s say in Go or now also in chess and shogi,

it’s not sufficient to learn an evaluation for a state

because the value of an information set

depends not only on the exact state,

but it also depends on both players beliefs.

Like if I have a bad hand,

I’m much better off if the opponent thinks I have a good hand

and vice versa.

If I have a good hand,

I’m much better off if the opponent believes

I have a bad hand.

So the value of a state is not just a function of the cards.

It depends on, if you will, the path of play,

but only to the extent that it’s captured

in the belief distributions.

So that’s why it’s not as simple

as it is in perfect information games.

And I don’t wanna say it’s simple there either.

It’s of course very complicated computationally there too,

but at least conceptually, it’s very straightforward.

There’s a state, there’s an evaluation function.

You can try to learn it.

Here, you have to do something more.

And what we do is in one of these papers,

we’re looking at where we allow the opponent

to actually take different strategies

at the leaf of the search tree, if you will.

And that is a different way of doing it.

And it doesn’t assume therefore a particular way

that the opponent plays,

but it allows the opponent to choose

from a set of different continuation strategies.

And that forces us to not be too optimistic

in a look ahead search.

And that’s one way you can do sound look ahead search

in imperfect information games,

which is very difficult.

And you were asking about DeepStack.

What they did, it was very different than what we do,

either in Libratus or in this new work.

They were randomly generating various situations

in the game.

Then they were doing the look ahead

from there to the end of the game,

as if that was the start of a different game.

And then they were using deep learning

to learn those values of those states,

but the states were not just the physical states.

They include belief distributions.

When you talk about look ahead for DeepStack

or with Libratus, does it mean,

considering every possibility that the game can evolve,

are we talking about extremely,

sort of this exponentially growth of a tree?

Yes, so we’re talking about exactly that.

Much like you do in alpha beta search

or Monte Carlo tree search, but with different techniques.

So there’s a different search algorithm.

And then we have to deal with the leaves differently.

So if you think about what Libratus did,

we didn’t have to worry about this

because we only did it at the end of the game.

So we would always terminate into a real situation

and we would know what the payout is.

It didn’t do these depth limited lookaheads,

but now in this new paper, which is called depth limited,

I think it’s called depth limited search

for imperfect information games,

we can actually do sound depth limited lookahead.

So we can actually start to do the look ahead

from the beginning of the game on,

because that’s too complicated to do

for this whole long game.

So in Libratus, we were just doing it for the end.

So, and then the other side, this belief distribution,

so is it explicitly modeled what kind of beliefs

that the opponent might have?

Yeah, it is explicitly modeled, but it’s not assumed.

The beliefs are actually output, not input.

Of course, the starting beliefs are input,

but they just fall from the rules of the game

because we know that the dealer deals uniformly

from the deck, so I know that every pair of cards

that you might have is equally likely.

I know that for a fact, that just follows

from the rules of the game.

Of course, except the two cards that I have,

I know you don’t have those.


You have to take that into account.

That’s called card removal and that’s very important.

Is the dealing always coming from a single deck

in Heads Up, so you can assume.

Single deck, so you know that if I have the ace of spades,

I know you don’t have an ace of spades.

Great, so in the beginning, your belief is basically

the fact that it’s a fair dealing of hands,

but how do you start to adjust that belief?

Well, that’s where this beauty of game theory comes.

So Nash equilibrium, which John Nash introduced in 1950,

introduces what rational play is

when you have more than one player.

And these are pairs of strategies

where strategies are contingency plans,

one for each player.

So that neither player wants to deviate

to a different strategy,

given that the other doesn’t deviate.

But as a side effect, you get the beliefs from base roll.

So Nash equilibrium really isn’t just deriving

in these imperfect information games,

Nash equilibrium, it doesn’t just define strategies.

It also defines beliefs for both of us

and defines beliefs for each state.

So at each state, it’s called information sets.

At each information set in the game,

there’s a set of different states that we might be in,

but I don’t know which one we’re in.

Nash equilibrium tells me exactly

what is the probability distribution

over those real world states in my mind.

How does Nash equilibrium give you that distribution?

So why?

I’ll do a simple example.

So you know the game Rock, Paper, Scissors?

So we can draw it as player one moves first

and then player two moves.

But of course, it’s important that player two

doesn’t know what player one moved,

otherwise player two would win every time.

So we can draw that as an information set

where player one makes one of three moves first,

and then there’s an information set for player two.

So player two doesn’t know which of those nodes

the world is in.

But once we know the strategy for player one,

Nash equilibrium will say that you play 1 3rd Rock,

1 3rd Paper, 1 3rd Scissors.

From that, I can derive my beliefs on the information set

that they’re 1 3rd, 1 3rd, 1 3rd.

So Bayes gives you that.

Bayes gives you.

But is that specific to a particular player,

or is it something you quickly update

with the specific player?

No, the game theory isn’t really player specific.

So that’s also why we don’t need any data.

We don’t need any history

how these particular humans played in the past

or how any AI or human had played before.

It’s all about rationality.

So the AI just thinks about

what would a rational opponent do?

And what would I do if I am rational?

And that’s the idea of game theory.

So it’s really a data free, opponent free approach.

So it comes from the design of the game

as opposed to the design of the player.

Exactly, there’s no opponent modeling per se.

I mean, we’ve done some work on combining opponent modeling

with game theory so you can exploit weak players even more,

but that’s another strand.

And in Librarus, we didn’t turn that on.

So I decided that these players are too good.

And when you start to exploit an opponent,

you typically open yourself up to exploitation.

And these guys have so few holes to exploit

and they’re world’s leading experts in counter exploitation.

So I decided that we’re not gonna turn that stuff on.

Actually, I saw a few of your papers exploiting opponents.

It sounded very interesting to explore.

Do you think there’s room for exploitation

generally outside of Librarus?

Is there a subject or people differences

that could be exploited, maybe not just in poker,

but in general interactions and negotiations,

all these other domains that you’re considering?

Yeah, definitely.

We’ve done some work on that.

And I really like the work at hybrid digested too.

So you figure out what would a rational opponent do.

And by the way, that’s safe in these zero sum games,

two player zero sum games,

because if the opponent does something irrational,

yes, it might throw off my beliefs,

but the amount that the player can gain

by throwing off my belief is always less

than they lose by playing poorly.

So it’s safe.

But still, if somebody’s weak as a player,

you might wanna play differently to exploit them more.

So you can think about it this way,

a game theoretic strategy is unbeatable,

but it doesn’t maximally beat the other opponent.

So the winnings per hand might be better

with a different strategy.

And the hybrid is that you start

from a game theoretic approach.

And then as you gain data about the opponent

in certain parts of the game tree,

then in those parts of the game tree,

you start to tweak your strategy more and more

towards exploitation while still staying fairly close

to the game theoretic strategy

so as to not open yourself up to exploitation too much.

How do you do that?

Do you try to vary up strategies, make it unpredictable?

It’s like, what is it, tit for tat strategies

in Prisoner’s Dilemma or?

Well, that’s a repeated game.

Repeated games.

Simple Prisoner’s Dilemma, repeated games.

But even there, there’s no proof that says

that that’s the best thing.

But experimentally, it actually does well.

So what kind of games are there, first of all?

I don’t know if this is something

that you could just summarize.

There’s perfect information games

where all the information’s on the table.

There is imperfect information games.

There’s repeated games that you play over and over.

There’s zero sum games.

There’s non zero sum games.

And then there’s a really important distinction

you’re making, two player versus more players.

So what are, what other games are there?

And what’s the difference, for example,

with this two player game versus more players?

What are the key differences in your view?

So let me start from the basics.

So a repeated game is a game where the same exact game

is played over and over.

In these extensive form games, where it’s,

think about three form, maybe with these information sets

to represent incomplete information,

you can have kind of repetitive interactions.

Even repeated games are a special case of that, by the way.

But the game doesn’t have to be exactly the same.

It’s like in sourcing auctions.

Yes, we’re gonna see the same supply base year to year,

but what I’m buying is a little different every time.

And the supply base is a little different every time

and so on.

So it’s not really repeated.

So to find a purely repeated game

is actually very rare in the world.

So they’re really a very course model of what’s going on.

Then if you move up from just repeated,

simple repeated matrix games,

not all the way to extensive form games,

but in between, they’re stochastic games,

where, you know, there’s these,

you think about it like these little matrix games.

And when you take an action and your opponent takes an action,

they determine not which next state I’m going to,

next game I’m going to,

but the distribution over next games

where I might be going to.

So that’s the stochastic game.

But it’s like matrix games, repeated stochastic games,

extensive form games.

That is from less to more general.

And poker is an example of the last one.

So it’s really in the most general setting.

Extensive form games.

And that’s kind of what the AI community has been working on

and being benchmarked on

with this Heads Up No Limit Texas Holdem.

Can you describe extensive form games?

What’s the model here?

Yeah, so if you’re familiar with the tree form,

so it’s really the tree form.

Like in chess, there’s a search tree.

Versus a matrix.

Versus a matrix, yeah.

And the matrix is called the matrix form

or bi matrix form or normal form game.

And here you have the tree form.

So you can actually do certain types of reasoning there

that you lose the information when you go to normal form.

There’s a certain form of equivalence.

Like if you go from tree form and you say it,

every possible contingency plan is a strategy.

Then I can actually go back to the normal form,

but I lose some information from the lack of sequentiality.

Then the multiplayer versus two player distinction

is an important one.

So two player games in zero sum

are conceptually easier and computationally easier.

They’re still huge like this one,

but they’re conceptually easier and computationally easier

in that conceptually, you don’t have to worry about

which equilibrium is the other guy going to play

when there are multiple,

because any equilibrium strategy is a best response

to any other equilibrium strategy.

So I can play a different equilibrium from you

and we’ll still get the right values of the game.

That falls apart even with two players

when you have general sum games.

Even without cooperation just in general.

Even without cooperation.

So there’s a big gap from two player zero sum

to two player general sum or even to three player zero sum.

That’s a big gap, at least in theory.

Can you maybe non mathematically provide the intuition

why it all falls apart with three or more players?

It seems like you should still be able to have

a Nash equilibrium that’s instructive, that holds.

Okay, so it is true that all finite games

have a Nash equilibrium.

So this is what John Nash actually proved.

So they do have a Nash equilibrium.

That’s not the problem.

The problem is that there can be many.

And then there’s a question of which equilibrium to select.

So, and if you select your strategy

from a different equilibrium and I select mine,

then what does that mean?

And in these non zero sum games,

we may lose some joint benefit

by being just simply stupid.

We could actually both be better off

if we did something else.

And in three player, you get other problems

also like collusion.

Like maybe you and I can gang up on a third player

and we can do radically better by colluding.

So there are lots of issues that come up there.

So Noah Brown, the student you work with on this

has mentioned, I looked through the AMA on Reddit.

He mentioned that the ability of poker players

to collaborate will make the game.

He was asked the question of,

how would you make the game of poker,

or both of you were asked the question,

how would you make the game of poker

beyond being solvable by current AI methods?

And he said that there’s not many ways

of making poker more difficult,

but a collaboration or cooperation between players

would make it extremely difficult.

So can you provide the intuition behind why that is,

if you agree with that idea?

Yeah, so I’ve done a lot of work on coalitional games

and we actually have a paper here

with my other student Gabriele Farina

and some other collaborators at NIPS on that.

Actually just came back from the poster session

where we presented this.

But so when you have a collusion, it’s a different problem.

And it typically gets even harder then.

Even the game representations,

some of the game representations don’t really allow

good computation.

So we actually introduced a new game representation

for that.

Is that kind of cooperation part of the model?

Are you, do you have, do you have information

about the fact that other players are cooperating

or is it just this chaos that where nothing is known?

So there’s some things unknown.

Can you give an example of a collusion type game

or is it usually?

So like bridge.

So think about bridge.

It’s like when you and I are on a team,

our payoffs are the same.

The problem is that we can’t talk.

So when I get my cards, I can’t whisper to you

what my cards are.

That would not be allowed.

So we have to somehow coordinate our strategies

ahead of time and only ahead of time.

And then there’s certain signals we can talk about,

but they have to be such that the other team

also understands them.

So that’s an example where the coordination

is already built into the rules of the game.

But in many other situations like auctions

or negotiations or diplomatic relationships, poker,

it’s not really built in, but it still can be very helpful

for the colluders.

I’ve read you write somewhere,

the negotiations you come to the table with prior,

like a strategy that you’re willing to do

and not willing to do those kinds of things.

So how do you start to now moving away from poker,

moving beyond poker into other applications

like negotiations, how do you start applying this

to other domains, even real world domains

that you’ve worked on?

Yeah, I actually have two startup companies

doing exactly that.

One is called Strategic Machine,

and that’s for kind of business applications,

gaming, sports, all sorts of things like that.

Any applications of this to business and to sports

and to gaming, to various types of things

in finance, electricity markets and so on.

And the other is called Strategy Robot,

where we are taking these to military security,

cyber security and intelligence applications.

I think you worked a little bit in,

how do you put it, advertisement,

sort of suggesting ads kind of thing, auction.

That’s another company, optimized markets.

But that’s much more about a combinatorial market

and optimization based technology.

That’s not using these game theoretic reasoning technologies.

I see, okay, so what sort of high level

do you think about our ability to use

game theoretic concepts to model human behavior?

Do you think human behavior is amenable

to this kind of modeling outside of the poker games,

and where have you seen it done successfully in your work?

I’m not sure the goal really is modeling humans.

Like for example, if I’m playing a zero sum game,

I don’t really care that the opponent

is actually following my model of rational behavior,

because if they’re not, that’s even better for me.

Right, so see with the opponents in games,

the prerequisite is that you formalize

the interaction in some way

that can be amenable to analysis.

And you’ve done this amazing work with mechanism design,

designing games that have certain outcomes.

But, so I’ll tell you an example

from my world of autonomous vehicles, right?

We’re studying pedestrians,

and pedestrians and cars negotiate

in this nonverbal communication.

There’s this weird game dance of tension

where pedestrians are basically saying,

I trust that you won’t kill me,

and so as a jaywalker, I will step onto the road

even though I’m breaking the law, and there’s this tension.

And the question is, we really don’t know

how to model that well in trying to model intent.

And so people sometimes bring up ideas

of game theory and so on.

Do you think that aspect of human behavior

can use these kinds of imperfect information approaches,

modeling, how do you start to attack a problem like that

when you don’t even know how to design the game

to describe the situation in order to solve it?

Okay, so I haven’t really thought about jaywalking,

but one thing that I think could be a good application

in autonomous vehicles is the following.

So let’s say that you have fleets of autonomous cars

operating by different companies.

So maybe here’s the Waymo fleet and here’s the Uber fleet.

If you think about the rules of the road,

they define certain legal rules,

but that still leaves a huge strategy space open.

Like as a simple example, when cars merge,

how humans merge, they slow down and look at each other

and try to merge.

Wouldn’t it be better if these situations

would already be prenegotiated

so we can actually merge at full speed

and we know that this is the situation,

this is how we do it, and it’s all gonna be faster.

But there are way too many situations to negotiate manually.

So you could use automated negotiation,

this is the idea at least,

you could use automated negotiation

to negotiate all of these situations

or many of them in advance.

And of course it might be that,

hey, maybe you’re not gonna always let me go first.

Maybe you said, okay, well, in these situations,

I’ll let you go first, but in exchange,

you’re gonna give me too much,

you’re gonna let me go first in this situation.

So it’s this huge combinatorial negotiation.

And do you think there’s room in that example of merging

to model this whole situation

as an imperfect information game

or do you really want to consider it to be a perfect?

No, that’s a good question, yeah.

That’s a good question.

Do you pay the price of assuming

that you don’t know everything?

Yeah, I don’t know.

It’s certainly much easier.

Games with perfect information are much easier.

So if you can’t get away with it, you should.

But if the real situation is of imperfect information,

then you’re gonna have to deal with imperfect information.

Great, so what lessons have you learned

the Annual Computer Poker Competition?

An incredible accomplishment of AI.

You look at the history of Deep Blue, AlphaGo,

these kind of moments when AI stepped up

in an engineering effort and a scientific effort combined

to beat the best of human players.

So what do you take away from this whole experience?

What have you learned about designing AI systems

that play these kinds of games?

And what does that mean for AI in general,

for the future of AI development?

Yeah, so that’s a good question.

So there’s so much to say about it.

I do like this type of performance oriented research.

Although in my group, we go all the way from like idea

to theory, to experiments, to big system building,

to commercialization, so we span that spectrum.

But I think that in a lot of situations in AI,

you really have to build the big systems

and evaluate them at scale

before you know what works and doesn’t.

And we’ve seen that in the computational

game theory community, that there are a lot of techniques

that look good in the small,

but then they cease to look good in the large.

And we’ve also seen that there are a lot of techniques

that look superior in theory.

And I really mean in terms of convergence rates,

like first order methods, better convergence rates,

like the CFR based algorithms,

yet the CFR based algorithms are the fastest in practice.

So it really tells me that you have to test this in reality.

The theory isn’t tight enough, if you will,

to tell you which algorithms are better than the others.

And you have to look at these things in the large,

because any sort of projections you do from the small

can at least in this domain be very misleading.

So that’s kind of from a kind of a science

and engineering perspective, from a personal perspective,

it’s been just a wild experience

in that with the first poker competition,

the first brains versus AI,

man machine poker competition that we organized.

There had been, by the way, for other poker games,

there had been previous competitions,

but this was for Heads Up No Limit, this was the first.

And I probably became the most hated person

in the world of poker.

And I didn’t mean to, I just saw.

Why is that?

For cracking the game, for something.

Yeah, a lot of people felt that it was a real threat

to the whole game, the whole existence of the game.

If AI becomes better than humans,

people would be scared to play poker

because there are these superhuman AIs running around

taking their money and all of that.

So I just, it’s just really aggressive.

The comments were super aggressive.

I got everything just short of death threats.

Do you think the same was true for chess?

Because right now they just completed

the world championships in chess,

and humans just started ignoring the fact

that there’s AI systems now that outperform humans

and they still enjoy the game, it’s still a beautiful game.

That’s what I think.

And I think the same thing happens in poker.

And so I didn’t think of myself

as somebody who was gonna kill the game,

and I don’t think I did.

I’ve really learned to love this game.

I wasn’t a poker player before,

but learned so many nuances about it from these AIs,

and they’ve really changed how the game is played,

by the way.

So they have these very Martian ways of playing poker,

and the top humans are now incorporating

those types of strategies into their own play.

So if anything, to me, our work has made poker

a richer, more interesting game for humans to play,

not something that is gonna steer humans

away from it entirely.

Just a quick comment on something you said,

which is, if I may say so,

in academia is a little bit rare sometimes.

It’s pretty brave to put your ideas to the test

in the way you described,

saying that sometimes good ideas don’t work

when you actually try to apply them at scale.

So where does that come from?

I mean, if you could do advice for people,

what drives you in that sense?

Were you always this way?

I mean, it takes a brave person.

I guess is what I’m saying, to test their ideas

and to see if this thing actually works

against human top human players and so on.

Yeah, I don’t know about brave,

but it takes a lot of work.

It takes a lot of work and a lot of time

to organize, to make something big

and to organize an event and stuff like that.

And what drives you in that effort?

Because you could still, I would argue,

get a best paper award at NIPS as you did in 17

without doing this.

That’s right, yes.

And so in general, I believe it’s very important

to do things in the real world and at scale.

And that’s really where the pudding, if you will,

proof is in the pudding, that’s where it is.

In this particular case,

it was kind of a competition between different groups

and for many years as to who can be the first one

to beat the top humans at Heads Up No Limit, Texas Holdem.

So it became kind of like a competition who can get there.

Yeah, so a little friendly competition

could do wonders for progress.

Yes, absolutely.

So the topic of mechanism design,

which is really interesting, also kind of new to me,

except as an observer of, I don’t know, politics and any,

I’m an observer of mechanisms,

but you write in your paper an automated mechanism design

that I quickly read.

So mechanism design is designing the rules of the game

so you get a certain desirable outcome.

And you have this work on doing so in an automatic fashion

as opposed to fine tuning it.

So what have you learned from those efforts?

If you look, say, I don’t know,

at complexes like our political system,

can we design our political system

to have, in an automated fashion,

to have outcomes that we want?

Can we design something like traffic lights to be smart

where it gets outcomes that we want?

So what are the lessons that you draw from that work?

Yeah, so I still very much believe

in the automated mechanism design direction.


But it’s not a panacea.

There are impossibility results in mechanism design

saying that there is no mechanism that accomplishes

objective X in class C.

So it’s not going to,

there’s no way using any mechanism design tools,

manual or automated,

to do certain things in mechanism design.

Can you describe that again?

So meaning it’s impossible to achieve that?

Yeah, yeah.

And it’s unlikely.


So these are not statements about human ingenuity

who might come up with something smart.

These are proofs that if you want to accomplish

properties X in class C,

that is not doable with any mechanism.

The good thing about automated mechanism design

is that we’re not really designing for a class.

We’re designing for specific settings at a time.

So even if there’s an impossibility result

for the whole class,

it just doesn’t mean that all of the cases

in the class are impossible.

It just means that some of the cases are impossible.

So we can actually carve these islands of possibility

within these known impossible classes.

And we’ve actually done that.

So one of the famous results in mechanism design

is the Meyerson Satethweight theorem

by Roger Meyerson and Mark Satethweight from 1983.

It’s an impossibility of efficient trade

under imperfect information.

We show that you can, in many settings,

avoid that and get efficient trade anyway.

Depending on how they design the game, okay.

Depending how you design the game.

And of course, it doesn’t in any way

contradict the impossibility result.

The impossibility result is still there,

but it just finds spots within this impossible class

where in those spots, you don’t have the impossibility.

Sorry if I’m going a bit philosophical,

but what lessons do you draw towards,

like I mentioned, politics or human interaction

and designing mechanisms for outside of just

these kinds of trading or auctioning

or purely formal games or human interaction,

like a political system?

How, do you think it’s applicable to, yeah, politics

or to business, to negotiations, these kinds of things,

designing rules that have certain outcomes?

Yeah, yeah, I do think so.

Have you seen that successfully done?

They haven’t really, oh, you mean mechanism design

or automated mechanism design?

Automated mechanism design.

So mechanism design itself

has had fairly limited success so far.

There are certain cases,

but most of the real world situations

are actually not sound from a mechanism design perspective,

even in those cases where they’ve been designed

by very knowledgeable mechanism design people,

the people are typically just taking some insights

from the theory and applying those insights

into the real world,

rather than applying the mechanisms directly.

So one famous example of is the FCC spectrum auctions.

So I’ve also had a small role in that

and very good economists have been working,

excellent economists have been working on that

with no game theory,

yet the rules that are designed in practice there,

they’re such that bidding truthfully

is not the best strategy.

Usually mechanism design,

we try to make things easy for the participants.

So telling the truth is the best strategy,

but even in those very high stakes auctions

where you have tens of billions of dollars

worth of spectrum being auctioned,

truth telling is not the best strategy.

And by the way,

nobody knows even a single optimal bidding strategy

for those auctions.

What’s the challenge of coming up with an optimal,

because there’s a lot of players and there’s imperfect.

It’s not so much that a lot of players,

but many items for sale,

and these mechanisms are such that even with just two items

or one item, bidding truthfully

wouldn’t be the best strategy.

If you look at the history of AI,

it’s marked by seminal events.

AlphaGo beating a world champion human Go player,

I would put Liberatus winning the Heads Up No Limit Holdem

as one of such event.

Thank you.

And what do you think is the next such event,

whether it’s in your life or in the broadly AI community

that you think might be out there

that would surprise the world?

So that’s a great question,

and I don’t really know the answer.

In terms of game solving,

Heads Up No Limit Texas Holdem

really was the one remaining widely agreed upon benchmark.

So that was the big milestone.

Now, are there other things?

Yeah, certainly there are,

but there’s not one that the community

has kind of focused on.

So what could be other things?

There are groups working on StarCraft.

There are groups working on Dota 2.

These are video games.

Or you could have like Diplomacy or Hanabi,

things like that.

These are like recreational games,

but none of them are really acknowledged

as kind of the main next challenge problem,

like chess or Go or Heads Up No Limit Texas Holdem was.

So I don’t really know in the game solving space

what is or what will be the next benchmark.

I kind of hope that there will be a next benchmark

because really the different groups

working on the same problem

really drove these application independent techniques

forward very quickly over 10 years.

Do you think there’s an open problem

that excites you that you start moving away

from games into real world games,

like say the stock market trading?

Yeah, so that’s kind of how I am.

So I am probably not going to work

as hard on these recreational benchmarks.

I’m doing two startups on game solving technology,

Strategic Machine and Strategy Robot,

and we’re really interested

in pushing this stuff into practice.

What do you think would be really

a powerful result that would be surprising

that would be, if you can say,

I mean, five years, 10 years from now,

something that statistically you would say

is not very likely,

but if there’s a breakthrough, would achieve?

Yeah, so I think that overall,

we’re in a very different situation in game theory

than we are in, let’s say, machine learning.

So in machine learning, it’s a fairly mature technology

and it’s very broadly applied

and proven success in the real world.

In game solving, there are almost no applications yet.

We have just become superhuman,

which machine learning you could argue happened in the 90s,

if not earlier,

and at least on supervised learning,

certain complex supervised learning applications.

Now, I think the next challenge problem,

I know you’re not asking about it this way,

you’re asking about the technology breakthrough,

but I think that big, big breakthrough

is to be able to show that, hey,

maybe most of, let’s say, military planning

or most of business strategy

will actually be done strategically

using computational game theory.

That’s what I would like to see

as the next five or 10 year goal.

Maybe you can explain to me again,

forgive me if this is an obvious question,

but machine learning methods,

neural networks suffer from not being transparent,

not being explainable.

Game theoretic methods, Nash equilibria,

do they generally, when you see the different solutions,

are they, when you talk about military operations,

are they, once you see the strategies,

do they make sense, are they explainable,

or do they suffer from the same problems

as neural networks do?

So that’s a good question.

I would say a little bit yes and no.

And what I mean by that is that

these game theoretic strategies,

let’s say, Nash equilibrium,

it has provable properties.

So it’s unlike, let’s say, deep learning

where you kind of cross your fingers,

hopefully it’ll work.

And then after the fact, when you have the weights,

you’re still crossing your fingers,

and I hope it will work.

Here, you know that the solution quality is there.

There’s provable solution quality guarantees.

Now, that doesn’t necessarily mean

that the strategies are human understandable.

That’s a whole other problem.

So I think that deep learning and computational game theory

are in the same boat in that sense,

that both are difficult to understand.

But at least the game theoretic techniques,

they have these guarantees of solution quality.

So do you see business operations, strategic operations,

or even military in the future being

at least the strong candidates

being proposed by automated systems?

Do you see that?

Yeah, I do, I do.

But that’s more of a belief than a substantiated fact.

Depending on where you land in optimism or pessimism,

that’s a really, to me, that’s an exciting future,

especially if there’s provable things

in terms of optimality.

So looking into the future,

there’s a few folks worried about the,

especially you look at the game of poker,

which is probably one of the last benchmarks

in terms of games being solved.

They worry about the future

and the existential threats of artificial intelligence.

So the negative impact in whatever form on society.

Is that something that concerns you as much,

or are you more optimistic about the positive impacts of AI?

Oh, I am much more optimistic about the positive impacts.

So just in my own work, what we’ve done so far,

we run the nationwide kidney exchange.

Hundreds of people are walking around alive today,

who would it be?

And it’s increased employment.

You have a lot of people now running kidney exchanges

and at the transplant centers,

interacting with the kidney exchange.

You have extra surgeons, nurses, anesthesiologists,

hospitals, all of that.

So employment is increasing from that

and the world is becoming a better place.

Another example is combinatorial sourcing auctions.

We did 800 large scale combinatorial sourcing auctions

from 2001 to 2010 in a previous startup of mine

called CombineNet.

And we increased the supply chain efficiency

on that $60 billion of spend by 12.6%.

So that’s over $6 billion of efficiency improvement

in the world.

And this is not like shifting value

from somebody to somebody else,

just efficiency improvement, like in trucking,

less empty driving, so there’s less waste,

less carbon footprint and so on.

So a huge positive impact in the near term,

but sort of to stay in it for a little longer,

because I think game theory has a role to play here.

Oh, let me actually come back on that as one thing.

I think AI is also going to make the world much safer.

So that’s another aspect that often gets overlooked.

Well, let me ask this question.

Maybe you can speak to the safer.

So I talked to Max Tegmark and Stuart Russell,

who are very concerned about existential threats of AI.

And often the concern is about value misalignment.

So AI systems basically working,

operating towards goals that are not the same

as human civilization, human beings.

So it seems like game theory has a role to play there

to make sure the values are aligned with human beings.

I don’t know if that’s how you think about it.

If not, how do you think AI might help with this problem?

How do you think AI might make the world safer?

Yeah, I think this value misalignment

is a fairly theoretical worry.

And I haven’t really seen it in,

because I do a lot of real applications.

I don’t see it anywhere.

The closest I’ve seen it

was the following type of mental exercise really,

where I had this argument in the late eighties

when we were building

these transportation optimization systems.

And somebody had heard that it’s a good idea

to have high utilization of assets.

So they told me, hey, why don’t you put that as objective?

And we didn’t even put it as an objective

because I just showed him that,

if you had that as your objective,

the solution would be to load your trucks full

and drive in circles.

Nothing would ever get delivered.

You’d have a hundred percent utilization.

So yeah, I know this phenomenon.

I’ve known this for over 30 years,

but I’ve never seen it actually be a problem in reality.

And yes, if you have the wrong objective,

the AI will optimize that to the hilt

and it’s gonna hurt more than some human

who’s kind of trying to solve it in a half baked way

with some human insight too.

But I just haven’t seen that materialize in practice.

There’s this gap that you’ve actually put your finger on

very clearly just now between theory and reality.

That’s very difficult to put into words, I think.

It’s what you can theoretically imagine,

the worst possible case or even, yeah, I mean bad cases.

And what usually happens in reality.

So for example, to me,

maybe it’s something you can comment on having grown up

and I grew up in the Soviet Union.

There’s currently 10,000 nuclear weapons in the world.

And for many decades,

it’s theoretically surprising to me

that the nuclear war is not broken out.

Do you think about this aspect

from a game theoretic perspective in general,

why is that true?

Why in theory you could see

how things would go terribly wrong

and somehow yet they have not?

Yeah, how do you think about it?

So I do think about that a lot.

I think the biggest two threats that we’re facing as mankind,

one is climate change and the other is nuclear war.

So those are my main two worries that I worry about.

And I’ve tried to do something about climate,

thought about trying to do something

for climate change twice.

Actually, for two of my startups,

I’ve actually commissioned studies

of what we could do on those things.

And we didn’t really find a sweet spot,

but I’m still keeping an eye out on that.

If there’s something where we could actually

provide a market solution or optimizations solution

or some other technology solution to problems.

Right now, like for example,

pollution critic markets was what we were looking at then.

And it was much more the lack of political will

by those markets were not so successful

rather than bad market design.

So I could go in and make a better market design,

but that wouldn’t really move the needle

on the world very much if there’s no political will.

And in the US, the market,

at least the Chicago market was just shut down and so on.

So then it doesn’t really help

how great your market design was.

And then the nuclear side, it’s more,

so global warming is a more encroaching problem.

Nuclear weapons have been here.

It’s an obvious problem that’s just been sitting there.

So how do you think about,

what is the mechanism design there

that just made everything seem stable?

And are you still extremely worried?

I am still extremely worried.

So you probably know the simple game theory of mad.

So this was a mutually assured destruction

and it doesn’t require any computation with small matrices.

You can actually convince yourself

that the game is such that nobody wants to initiate.

Yeah, that’s a very coarse grained analysis.

And it really works in a situational way.

You have two superpowers or small number of superpowers.

Now things are very different.

You have a smaller nuke.

So the threshold of initiating is smaller

and you have smaller countries and non nation actors

who may get a nuke and so on.

So I think it’s riskier now than it was maybe ever before.

And what idea, application of AI,

you’ve talked about a little bit,

but what is the most exciting to you right now?

I mean, you’re here at NIPS, NeurIPS.

Now you have a few excellent pieces of work,

but what are you thinking into the future

with several companies you’re doing?

What’s the most exciting thing or one of the exciting things?

The number one thing for me right now

is coming up with these scalable techniques

for game solving and applying them into the real world.

I’m still very interested in market design as well.

And we’re doing that in the optimized markets,

but I’m most interested if number one right now

is strategic machine strategy robot,

getting that technology out there

and seeing as you were in the trenches doing applications,

what needs to be actually filled,

what technology gaps still need to be filled.

So it’s so hard to just put your feet on the table

and imagine what needs to be done.

But when you’re actually doing real applications,

the applications tell you what needs to be done.

And I really enjoy that interaction.

Is it a challenging process to apply

some of the state of the art techniques you’re working on

and having the various players in industry

or the military or people who could really benefit from it

actually use it?

What’s that process like of,

autonomous vehicles work with automotive companies

and they’re in many ways are a little bit old fashioned.

It’s difficult.

They really want to use this technology.

There’s clearly will have a significant benefit,

but the systems aren’t quite in place

to easily have them integrated in terms of data,

in terms of compute, in terms of all these kinds of things.

So is that one of the bigger challenges that you’re facing

and how do you tackle that challenge?

Yeah, I think that’s always a challenge.

That’s kind of slowness and inertia really

of let’s do things the way we’ve always done it.

You just have to find the internal champions

at the customer who understand that,

hey, things can’t be the same way in the future.

Otherwise bad things are going to happen.

And it’s in autonomous vehicles.

It’s actually very interesting

that the car makers are doing that

and they’re very traditional,

but at the same time you have tech companies

who have nothing to do with cars or transportation

like Google and Baidu really pushing on autonomous cars.

I find that fascinating.

Clearly you’re super excited

about actually these ideas having an impact in the world.

In terms of the technology, in terms of ideas and research,

are there directions that you’re also excited about?

Whether that’s on some of the approaches you talked about

for the imperfect information games,

whether it’s applying deep learning

to some of these problems,

is there something that you’re excited

in the research side of things?

Yeah, yeah, lots of different things

in the game solving.

So solving even bigger games,

games where you have more hidden action

of the player actions as well.

Poker is a game where really the chance actions are hidden

or some of them are hidden,

but the player actions are public.

Multiplayer games of various sorts,

collusion, opponent exploitation,

all and even longer games.

So games that basically go forever,

but they’re not repeated.

So see extensive fun games that go forever.

What would that even look like?

How do you represent that?

How do you solve that?

What’s an example of a game like that?

Or is this some of the stochastic games

that you mentioned?

Let’s say business strategy.

So it’s not just modeling like a particular interaction,

but thinking about the business from here to eternity.

Or let’s say military strategy.

So it’s not like war is gonna go away.

How do you think about military strategy

that’s gonna go forever?

How do you even model that?

How do you know whether a move was good

that somebody made and so on?

So that’s kind of one direction.

I’m also very interested in learning

much more scalable techniques for integer programming.

So we had an ICML paper this summer on that.

The first automated algorithm configuration paper

that has theoretical generalization guarantees.

So if I see this many training examples

and I told my algorithm in this way,

it’s going to have good performance

on the real distribution, which I’ve not seen.

So, which is kind of interesting

that algorithm configuration has been going on now

for at least 17 years seriously.

And there has not been any generalization theory before.

Well, this is really exciting

and it’s a huge honor to talk to you.

Thank you so much, Tomas.

Thank you for bringing Labradus to the world

and all the great work you’re doing.

Well, thank you very much.

It’s been fun.

No more questions.

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