Tuomas Sandholm: Poker and Game Theory

The following is a conversation with Thomas Sandholm. He's a professor at Samuel and co creator of labradas, which is the first AI system to beat top human players in the game of heads up, no limit Texas hold'.

Em.

He has published over 450 papers on game theory and machine learning, including a best paper in 2017 at NIPS, now renamed to New Reps, 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 lexfriedman 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 hold'. Em? Heads up Texas hold' Em. For people who might not be familiar this card game.

Yeah, happy to. So heads up, no limit Texas hold' Em 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, 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 going to be heads up, no limit Texas hold'. Em. It might be no limit takes us hold them 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 in 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 hold' Em there's a two cards that you only see they belong to you and there is they gradually lay out some cards that add up overall to five cards that everybody can see yeah. The imperfect nature of the information is the two cards that you're holding up front.

Yeah. So as you said, you know, you first get two cards in private each, and then you. 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 fifth 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. 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 it'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. 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, librettas. How do you pronounce it?

Libratus.

Libratus. Libratus.

Beats little Latin there.

A little bit of Latin brought us beat 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 studied?

Yeah. So the event was that we invited four of the top 10 players. These are 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 Hemans 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, you were keeping track of the money and Lebratus won 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? 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. Yes, 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 that 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, great question. So 18 months earlier I had organized a similar brains versus AI competition with a previous AI called Cloudical 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, 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 5050 shot and the international betting sites put us as a 4 to 1 or 5 to 1 underdog. So it's kind of interesting that people really believe in people over AI. People don't just over believing themselves, but they have overconfidence in other people as well compared to the performance of AI. And yeah, so we were a 4 to 1 or 5 to 1 underdog. And even after three days of beating the humans in a row, we were still 5050 on the international betting sites.

Do you think there's something special and magical about poker in the way people think about it, in the sense you have. I mean, even in chess, there's no Hollywood movies. Poker is this 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. The 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. Until you've seen it over perform 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, tell tellers are going to 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 tellers become much smaller and smaller aspect of the game. As you go to the top levels.

The amount of strategies, the amounts 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. There has been. 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 want to 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 is betting strategies.

Betting actions.

Yeah, baiting actions.

So there's information abstraction to 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, 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 used it for the first couple of betting actions.

So what's more important, the strength of the hand. So the information abstraction or 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 hold'.

Em.

Because if we both go all in, it's a huge stack of variants. So there are these massive swings in no limit decks as all. 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 your opponents didn't know that, how well would you be able to do.

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.

Yes.

So Libratus does not use, as far as I understand, use learning methods. Deep learning. Is there room for learning in. There's no reason why Lebratus 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, Deep Stack, the engine that does use deep learning that is unclear how well it does, but nevertheless uses deep learning. So what are your thoughts about learning methods to aid in the way that Libratus plays the game of poker?

Yeah, so as you said, Libratus 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.

Excellent.

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 want to 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 allowing 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 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 the belief distributions.

When you talk about lookahead or deep stack 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 crawl 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, 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. Yes, 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. Yes, 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. You know that if somebody, if, 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 Bayes rule. So Nash equilibrium really isn't just deriving in these imperfect information games. Nash equilibrium doesn't just define strategies. It also defines beliefs for both of us and defines beliefs for each state. So each state 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 1 moves first and then Player 2 moves. But of course, it's important that Player 2 doesn't know what Player 1 moved, otherwise Player 2 would win every time. So we can draw that as an information set where player one makes one or 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 1/3 rock, 1/3 paper, 1/3 scissors. From that I can derive my beliefs on the information set that they're 1/3, 1/3, 1/3.

So Bayes gives you.

That gives you.

But is that specific to a particular player or is it, is that something you quickly update with those?

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 we just think, 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 Libratus we didn't turn that on because 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 going to turn that stuff on.

Actually I saw a few of your papers. Exploiting opponents sound very interesting to explore. Do you think there's room for exploitation generally outside of Labradors? Is there subject or people differences that could be exploited? Maybe not just in poker, but in general interactions, negotiations, all these other domains that you're considering?

Yeah, definitely. We've done some work on that and I really like the work that hybridizes the two. So you figure out what would a rational opponent do and by the way, that's safe in these zero sum games, Two players, 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 want to 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 opponents. 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 theory 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, Italian?

That's a repeated game kind of 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 is 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 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 you?

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 think about tree 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 going to 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 coarse 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 there's 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, so that's the stochastic game, but it's like matrix games, repeated stochastic games, extensive form games, I.e. from less to more general. And poker is an example of the last one. So it's really in the most general settings, 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 text has hold.

Can you describe extensive form games? What's the motto 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 again. 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 the 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 a general sum games even without cooperation. Just even without cooperation. So there's a big gap from 2 player 0 sum to 2 player general sum or even to 3 player 0 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. Yeah, 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.

Yes.

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 no. 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 would 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 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 collisional 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. 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? 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. Something's 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 are certain signals we can talk about, but they have to be such that the other team also understands the. 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 with negotiations, you come to the table with priority, like a strategy that. Like 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. 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, cybersecurity 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.

Yes, 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 high sort of high level do you think about our ability to use game theoretic concepts to model human behavior? Do you think, do you think human behavior is amenable to this kind of modeling? So 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 there's a. 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, from my world of autonomous vehicles, right? We're studying pedestrians and pedestrians and cars negotiate in this non verbal 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 we, how do you start to attack a problem like that when you don't even know how the game 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, you know 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 pre negotiated 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 going to 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 going to always let me go first. Maybe you said, okay, well in these situations I'll let you go first, but in exchange you're going to give me two hours, you're going to 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 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 get away with it, you should. But if the real situation is of imperfect information, then you're going to have to deal with imperfect information.

Great. So what lessons have you learned? The annual computer poker competition, an incredible accomplishment of AI. You know, 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 sort of AI in general, for the future of AI development?

Yeah, so that's a good question. 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 better, like first order methods better Convergence rates like the CFR based 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, 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 vs. AI 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.

Why is that cracking the game, for example?

Yeah, it was. A lot of people, 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 it was 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's going to 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 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 going to 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, 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, do 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.

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 for many years as to who can be the first one to beat the top humans at heads up, no limit access, hold them. So it became, it became kind of like a competition who can get there.

Yeah. So a little friendly competition can 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 complex 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. Yes. 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 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.

Likely impossible. 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 Myerson Satterthwaite Theorem by Roger Myerson and mark Satterthwaite 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 you design the game.

Okay, so depending how you design the game. And of course it doesn't in any way, 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. What. How can, do you think it's applicable to 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 success that successfully done?

They haven't really. Oh, you mean mechanism design or automated mechanism?

Automated mechanism design.

So. 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 auction. So I've also had a small role in that and very good economists have been excellent economists have been working on that. With no game theory yet, the rules that are designed in practice there, they're such that being truthful 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.

Not a lot of players, but many items for sale. And these mechanisms are such that even with just two items or one item being truthfully wouldn't be the best strategy.

If you look at the history of AI, it's marked by seminal events and AlphaGo being a world champion human go player, I would put Lebradas winning the heads up, no limit hold' em 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 Holden 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 is 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, you know, 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 limitx as Holden was. So I don't really know in the game solving space what is or what will 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, 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 it's, you know, 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.

Yes.

So in machine learning, it's a fairly mature technology and it's very, 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 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 a next five or ten 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, you know, 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, disprovable 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 theory techniques, they have these guarantees of quality guarantees.

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 effect depending on where you.

Land 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 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 wouldn't be? And it's increased employment. You have a lot of people now running kidney exchanges and at 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.

This is 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.

Let me actually come back on. That is 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, 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 any 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 80s 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 100% 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 going to 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, you know, 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 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 optimization solution or some other technology solution to problems right now, like for example, pollution, credit 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 shows Chicago market was just shut down and so on. So then it doesn't really help how great your market design was.

And on 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 situation where 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 nukes 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 new RIPS 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 are 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, you know, in autonomous vehicles we work with automotive companies and they're in, 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 do you, 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, 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 the some of the approaches you talked about for imperfect information games, whether it's applying deep learning, just some of these problems. Is there something that you're excited in, 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 and even longer games. Some games that basically go forever, but they're not repeated. So see extensive form 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? This is some of the stochastic games that you mentioned.

Let's say business strategy and not just modeling 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 going to go away. How do you think about military strategy that's going to 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 these many training examples and I tool my algorithm in this way, it's going to have good performance on the real distribution, which I've not seen, 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 Labratus to the world and all the great work you're doing.

Well, thank you very much. It's been fun. Good questions.

Sa.