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McV4a6umbAY | a lot of the breakthroughs in AI. Actually, all AI did not use any deep learning, no deep learning at all. But I would also argue that a big reason for why all these AIs are superhuman in various games like chess, Go, backgammon even, is because they use real-time planning. The planning component is huge. In AlphaGo, for example, use Monte-Carlo Tree Search, | 360 | 381 | https://www.youtube.com/watch?v=McV4a6umbAY&t=360s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | in Deep Blue, it used Alpha-beta pruning. So, in fact, if you look at AlphaZero, without real-time planning, I guess this is washed out, but it ends up being right around there without Monte-Carlo Tree Search during real-time. Top human performance is right around here. So, in fact, without Monte-Carlo Tree Search, AlphaZero is not superhuman. The tree search gets you 2,000 ELO addition. | 381 | 409 | https://www.youtube.com/watch?v=McV4a6umbAY&t=381s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | So, real-time planning is really important, not just in Go, but also in poker, it turns out. This is actually the key breakthrough that allowed us to be top humans is figuring out how to do real-time planning. But it turns out that in poker, it ends up being way harder which is where it gets you right now. So in perfect-information games, you take some action, | 409 | 428 | https://www.youtube.com/watch?v=McV4a6umbAY&t=409s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | your opponent takes some action, you find yourself in a particularly subgame. Now, you can forget about everything that came before, all the other situations you did not encountered. The only thing that matters is the situation that you're in, and the situations that can be reached from this point on. So in perfect-information games, so for example, if I were to show you this chess board, | 428 | 452 | https://www.youtube.com/watch?v=McV4a6umbAY&t=428s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | you don't have to know how we ended up in this situation, you don't have to know about the Sicilian defense of the Queen's gambit. You can just look at this board, and if you're white, you can say, ''Okay, well, if I do a search, I can see if I move my white queen there, then it's checkmate, and the game is over. So, I should just do that. You don't have to know anything about the strategy of chess. | 452 | 468 | https://www.youtube.com/watch?v=McV4a6umbAY&t=452s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | But in imperfect-information games, if you take some action, and your opponent takes some action, and you find yourself in a particularly sub-game, now some other sub game that you are not in, and in fact, you might not even be able to reach from this point on, can affect what the optimal strategy is for the sub-game that you are in. This is counter-intuitive, but I'm going to give you | 468 | 488 | https://www.youtube.com/watch?v=McV4a6umbAY&t=468s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | a concrete example in a little bit that illustrates this. Now, before I get to that, I want to talk a little bit about what our goal is in these games. Our goal is to find a Nash equilibrium which in-two player zero-sum games, is the same thing as a min-max equilibrium. I won't get too technical about the definition, but basically, in a two-player zero-sum game, | 488 | 507 | https://www.youtube.com/watch?v=McV4a6umbAY&t=488s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | if you're playing the Nash equilibrium, you are guaranteed to not lose an expectation. Now, it's not always easy to find a Nash equilibrium, but it's always guaranteed to exist and a finite two-player zero-sum game. So, for example, in rock, paper, scissors, the Nash equilibrium is to this mix randomly between rock, paper, and scissors, with equal probability, | 507 | 523 | https://www.youtube.com/watch?v=McV4a6umbAY&t=507s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | because if you do that, then no matter what your opponent does, you will not lose an expectation. Now, in rock, paper, scissors, that also means you're not going to win an expectation, but in a complicated game like poker where there's a lot of sub-optimal actions that aren't actually played in the Nash equilibrium, it's likely that your opponent will make mistakes | 523 | 539 | https://www.youtube.com/watch?v=McV4a6umbAY&t=523s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and you will end up in practice winning as well. Yes. >> How important is it going to be to play a game So, if I compare this to say, heads up or not. If I got a heads up, if I got to sort of thinking about like this will go about seven players. >> That is a great question. So, I'll get to this, let's talk about this now. In poker, it doesn't really matter. So, in poker, if you were to use | 539 | 563 | https://www.youtube.com/watch?v=McV4a6umbAY&t=539s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | these same techniques for six player poker, you would almost certainly win. That said in general, poker is a special game because, I don't know if you play poker but two special things about poker. One is, it's really hard to collaborate with other players. So, you can't say, "Hey, let's team up against this other person at the table." In fact, if you try to do that, | 563 | 582 | https://www.youtube.com/watch?v=McV4a6umbAY&t=563s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | that'll be against the rules of poker. The other thing that's unique about poker is that people fold in the game. So, even if you have six players at the start of the game, it very quickly comes down to two players because people fold. So, you can use these techniques that are only guaranteed for two-player zero-sum games and it will just work in six player poker. | 582 | 600 | https://www.youtube.com/watch?v=McV4a6umbAY&t=582s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | But a big challenge is extending these techniques to other games that do allow for collaboration. In that, we don't really have a good approach for those games yet. So, for now, I'm just going to assume that we're working in the two-player zero-sum setting and it does extend in some cases to other situations as well. So, our goal is to find an approximate Nash equilibrium. | 600 | 626 | https://www.youtube.com/watch?v=McV4a6umbAY&t=600s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | We're going to measure performance in terms of exploitability. You can think of it as, distance from a Nash equilibrium, it's how well we would do against a worst-case adversary relative to if we had played a Nash equilibrium instead. So, how exploitable we are? I would argue that exploitability is actually extremely important and has been overlooked in the AI community as a whole. | 626 | 648 | https://www.youtube.com/watch?v=McV4a6umbAY&t=626s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | I think two recent man-machine matches actually really highlight this. One is the OpenAI, one versus one Dota2 Matches that you might have heard about, and the other is Fan Hui versus AlphaGo. In the OpenAI Matches, they made this AI that was able to beat top humans in one versus one Dota2 over three games. But after they won against the top human, they actually opened it up to the public and they invited | 648 | 672 | https://www.youtube.com/watch?v=McV4a6umbAY&t=648s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | random mediocre players to play against it to see if they could find any weaknesses. In fact, pretty quickly within a few thousand games, weak players were able to find certain tricks that they could basically fool the AI and figured out how to exploit it and beat it. Also, in Fan Hui versus AlphaGo, so they famously beat Fan Hui 5-0. But then after they published the Nature paper, | 672 | 694 | https://www.youtube.com/watch?v=McV4a6umbAY&t=672s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | they invited him to play several more matches against it to see if he could find out any weaknesses in the AI. In fact, he was able to find weaknesses where he was able to consistently beat the AI and they had to patch this before they released on the Nature. So, I think what this really demonstrates is that it's not enough to beat top humans in three or five or even 10 games. | 694 | 714 | https://www.youtube.com/watch?v=McV4a6umbAY&t=694s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | You really have to be able to consistently beat top humans, especially if you want to deploy an AI into the real world. If you're Microsoft and you're trying to deploy this products with real users, there's millions or billions of them, if there's a weakness, they're going to find it. But with the [inaudible] , we played the top humans not just in three or five hands of poker, | 714 | 733 | https://www.youtube.com/watch?v=McV4a6umbAY&t=714s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | we played them in 120,000 hands of poker over the course of 20 days. That whole time, all four players working as a team to try to exploit the AI in any way they could find. In fact, actually, I had lunch with one of the players, just a couple months ago. He said that the thing they found most shocking about the competition is that, at the end of each day, we gave them a log of all the hands that were | 733 | 755 | https://www.youtube.com/watch?v=McV4a6umbAY&t=733s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | played and we told them what the bot had on each hand that was played. This is big because in poker, a big part of the game is actually keeping your strategy hidden. If you fold, your opponents does see what cards you have. In fact, even if you don't fold but you lose the hand, you still don't show your cards are. So, you only see your opponent's hand about 20 percent, | 755 | 778 | https://www.youtube.com/watch?v=McV4a6umbAY&t=755s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | 25 percent of the time. So, like poker players will sometimes even call, just to see what their opponent had. But here, we're just giving them that information. We're telling them what the bot had on every single hand that it played. So, they didn't have to worry about that part all, and they found it absolutely amazing that they could not figure out how to exploit the AI, | 778 | 796 | https://www.youtube.com/watch?v=McV4a6umbAY&t=778s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | even though we were showing them the hands that the bot was playing every single time and the bot strategy wasn't really changing that much between days. All right, so I think exploitability is extremely important. I think has been overlooked by the AI community, and this is telling that the imperfect information game solving community has focused on throughout its existence. | 796 | 816 | https://www.youtube.com/watch?v=McV4a6umbAY&t=796s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | All right, so now, I want to get to the example of why imperfect information games are hard. I'm going to talk about a simple example that I call a Coin Toss. It starts with the coin flip. So, the coin is flipped that lands heads or tails with 50-50 probability. Player one is going to observe the outcome of the coin toss. Player two is not. So, after this coin lands, Player one has a choice. | 816 | 838 | https://www.youtube.com/watch?v=McV4a6umbAY&t=816s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | They can either sell the coin or they can choose play. We'll say, if they choose sell this to some separate subgame, the details of which are not important. The only thing that's important is the expected value. So, we'll say, if the coin landed heads, then the coin was lucky and they can sell it for 0.50 cents. On the other hand, if the coin landed it tails, | 838 | 856 | https://www.youtube.com/watch?v=McV4a6umbAY&t=838s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | we'll say it's unlucky and Player one loses 0.50 cents by selling it. On the other hand, they could choose play, and if they choose play, then it leads to Player two, and Player two has to then guess how the coin landed without having observed how it actually landed. So, if they guess correctly that is Player two guesses heads and the coin actually landed heads, | 856 | 877 | https://www.youtube.com/watch?v=McV4a6umbAY&t=856s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | then Player one is going to lose one dollar and Player two is going to gain one dollar. Here, the payoffs are shown for Player one because this is a two-player zero-sum game. So, Player two just receives the opposite payoff. Now, on the other hand, if Player two guesses incorrectly that is they guess tails and the coin actually landed heads, then Player one gains one dollar | 877 | 896 | https://www.youtube.com/watch?v=McV4a6umbAY&t=877s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and Player two loses one dollar. You can see there's a dotted line between the two players, two nodes this signifies that Player two is in what's called an information set. This means that Player two because they did not observe how the coin landed, they do not know which of those two states they were actually in. So, why do you imagine that you are Player two in | 896 | 914 | https://www.youtube.com/watch?v=McV4a6umbAY&t=896s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | this game and yeah, so why do you imagine that you are Player two in this game, you've just observed Player one chooses play action and so you know that you are in this imperfect information subgame. So, what should you do? Should you guess heads or should you guess tails? But one option is to just always guess heads. But if you do that, that's obviously a really bad strategy because now Player | 914 | 936 | https://www.youtube.com/watch?v=McV4a6umbAY&t=914s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | two can just sell the coin when it lands heads and get 0.50 cents, and choose play when the coin lands tails and gain a dollar. So, on average they're getting 0.75 cents. On the other hand, you could always choose tails, but that's also a really bad idea because now Player two can choose play when the coin lands heads and gain a dollar and choose sell when the coin lands | 936 | 959 | https://www.youtube.com/watch?v=McV4a6umbAY&t=936s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | in tails and lose 0.50 cents but it's better than losing a dollar. So, on average, they're still getting 0.25 cents in this game. So, it turns out that the optimal strategy is to mix. It's to guess heads with 25 percent probability and tails with 75 percent probability. If you do that, then no matter what Player one does, the best they can do is just break-even, | 959 | 980 | https://www.youtube.com/watch?v=McV4a6umbAY&t=959s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | get on average zero dollar in this game. So, this is the Nash equilibrium strategy for Player two in this game, at least for this subgame. But now, let's say we change the game a little bit. Let's say we changed the payoff for the sell action. So, now, an expectation Player one loses 0.50 cents for choosing sell when the coin lands heads, and gains 0.50 cents for choosing | 980 | 1,001 | https://www.youtube.com/watch?v=McV4a6umbAY&t=980s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | sell when the coin lands tails. Well, it's pretty easy to see that as Player two, your strategy in this subgame should now change as well. Now, you should be guessing heads with 75 percent probability and tails with 25 percent probability. But you can see what's happened here is that, by changing the expected value of the sell action, we have affected what the optimal strategy is in the play subgame. | 1,001 | 1,024 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1001s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Even though the sell action is not part of the play subgame and in fact, it's not even on the path leading to the play subgame. So, this is something that happens in imperfect information games. It does not happen in perfect information games. In perfect information games, if you wanted to determine the optimal strategy in subgame, you only need to look at that subgame by itself. | 1,024 | 1,043 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1024s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | But in imperfect information games, you have to look at the game as a whole. So, you can think of like perfect information games is a special case where you don't have to worry about all this stuff. Imperfect information games are the more general case where this is a problem. So, what do we do? Well, it turns out that we don't actually have to know the strategy for the entire game as a whole. | 1,043 | 1,065 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1043s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | I mentioned that this sell action leads to a subgame, where both players might take actions. But you don't have to worry about that, the only that really matters for determining the optimal strategy in this play subgame, is the expected value of Player one choosing sell. So, what we can do is try to estimate what that value is to Player one, and if we have that, | 1,065 | 1,085 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1065s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | then we can determine the optimal strategy in the play subgame. So, that's what we actually did in [inaudible]. We also have a theorem that says, "If this estimate is within delta of the true Nash equilibrium value, then we can solve for the play subgame and get within delta of the Nash Equilibrium." So, in the [inaudible] , we actually do this. We have this massive game | 1,085 | 1,109 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1085s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | which is simply way too large to solve upfront. So, we come up with a really good strategy just for the early part of the game, and we estimate what the optimal strategy is and what the expected values are in the later parts of the game. Now, when we're actually playing, we find ourselves in a particular subgame, we come up with a much better strategy for that particular subgame | 1,109 | 1,127 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1109s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | using information about the expected values from the other subgames. Then, we repeat this process, we just come up with a really good strategy for that early parts that are coming up and just estimate how to play in the later parts. We find ourselves in early subgame, we again compute a much better strategy and that particular subgame using information about the expected | 1,127 | 1,144 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1127s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | values of the other subgames. That's called nested subgame solving. This was the key breakthrough that allowed us to be top humans. So, when I, yes? >> Just [inaudible]. >> Yes, that's a great question. So, actually when we do this, this is sort of a general, how we would do this in general. But in poker, we solved the first two, there's four betting rounds. | 1,144 | 1,171 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1144s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | So, we solve the first two, with a pre-computed strategy. Because it's like each round grows exponentially in size. So, the first two rounds are actually pretty small. We got to the end of the second betting round, that's when we applied Subgame Solving. So, we came up with a much better strategy for the remainder of the game. We abstracted the bets. So, we want to consider | 1,171 | 1,190 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1171s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | all the 20,000 different bet sizes, we would just consider a small fraction of them. Then each time the opponent acted, each time they've made a bet, then we would solve a new subgame for that bet size. So, we would apply this recursive solving thing every time the opponent made an action beyond the second betting round. So, when I mention this idea of what's called Safe Subgame Solving, | 1,190 | 1,214 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1190s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | where we use the expected values from the other subgames, people always ask about this thing called Unsafe Subgame Solving, which is the more intuitive approach to doing this. The idea here is well, why don't we just estimate what the opponent strategy is? Let's say we can sort of like we played a bunch of hands against them or we can estimate what the Nash equilibrium is for them, | 1,214 | 1,231 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1214s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and we figured out, well, they should be choosing play 80 percent of the time when the coin lands heads and play 30 percent of the time when the coin lands tails. Let's say, just for example. Now, if we assume that the opponent's playing this strategy, can we then reason about the distribution of states that we might be in and then solve optimally using that distribution. | 1,231 | 1,250 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1231s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | It turns out that doesn't work. So, let me give you an example of what this would look like. When the coin lands either heads or tails, we reason that we're in one of these states with 50-50 probability. Now if we observe player one choose play, we would say, okay, well, in a Nash equilibrium, we would expect player one to choose play 80 percent of the time if we were in the left state, | 1,250 | 1,269 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1250s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | 30 percent of the time when we're in the tail state. So, we update our belief about what state we're in using Bayes rule, and now we can reason that we're in that left state with 73 percent probability, and in that right state with 27 percent probability. Now, we would just say, well, if we assume this distribution is correct, then the optimal strategy is to always choose heads. | 1,269 | 1,287 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1269s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | But if we've already established that's a really bad idea, because now the opponent can simply shift to selling the coin when it lands heads and choose and play with the coin lands tails. So, the problem with this approach is that we're making an assumption about how the opponent is playing. If it were true, like if this distribution were true that they were choosing | 1,287 | 1,305 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1287s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | play with 80 percent probability in heads and 30 percent probability in tails, then yes, we can apply this reasoning. But the opponent strategy can always change. They can always change adversarially to us. Yes? >> There's one thing that I've always been interested in, when you play the Nash or when you play against the opponent. It seems like they're not going to shift. | 1,305 | 1,323 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1305s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Even if you're playing the wrong strategy, they wouldn't exploit it off immediately. They have to learn to exploit it. I guess it's safe to definitely model the Nash, but I am curious about this intermediate space where you'd play against how they've been playing in the past, recognize that you need to shift in some way because they may shift as well. >> So, yeah, that's a great question. | 1,323 | 1,342 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1323s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | We actually did not, so one of the interesting things about humans playing poker, is that they're actually really good at exploiting. They are phenomenal at it. Way better than computers are currently. So, we actually did a competition against them in 2015 where we lost, and we would sometimes change the bot that they were playing against between days. Within 50 hands of playing, | 1,342 | 1,363 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1342s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | they could figure out how the bot had changed. So yes, if you can make an AI that could figure out how to do this better than humans, then that that might be valuable. But we're playing against really talented humans and we didn't think that we could beat them at that game, but then also why bother playing that game? Why bother trying to play that mind game if we can just | 1,363 | 1,383 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1363s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | approximate a Nash equilibrium and guarantee that we're going to win. So, I would argue that in the two player zero-sum game, if you want to beat top humans in a two-player zero-sum game, the best approach is to just approximate the Nash equilibrium because now, no matter what they're going to do, you're going to beat them. Now, I would argue that if your objectives are different, so for example, | 1,383 | 1,402 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1383s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | if you really want to beat up on a weak player and exploit them, then yeah, you don't want to necessarily play Nash equilibrium. You want to adapt to their weaknesses. This is challenging to do correctly, because if you try to adapt to a weak players weaknesses, you never know if they're just fooling you. Like if you're playing rock, paper, scissors against somebody and they | 1,402 | 1,419 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1402s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | throw rocks three times in a row, and you say, well, he's clearly an idiot who's throwing rock every single time, I'm going to throw paper next time, they could just throw scissors. So, there's no safe way that, except in special cases, there's no safe way to do that kind of opponent exploitation and still guarantee that you're going to beat top humans expectation. | 1,419 | 1,437 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1419s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | So, I think that is an excellent avenue for future research, but I think that in the two-player zero-sum setting, where we're just trying to beat top humans, I think this is the better way to go about it. So, Unsafe Subgame Solving, is very risky for this reason because if you make an assumption about how the opponent is playing, they can always shift to a different | 1,437 | 1,458 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1437s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | strategy and take advantage of that. Now, that said, it turns out that this actually works, yes, so we must account for the opponent's ability to adapt. Now, that said in practice, Unsafe Subgame Solving works unusually well in poker. It turns out that if you just approximate what the Nash Equilibrium strategy is and then assume that the opponent is playing that, | 1,458 | 1,480 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1458s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and apply Subgame solving in this way, that actually works really well in this domain. But we have found situations where this does not work well, and I think in more general settings, it would not do well. So, we actually use this in a few situations in Libratus. But in general, I would not recommend doing this. Unless the domain is specially structured that it would work. | 1,480 | 1,504 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1480s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | So, Safe Subgame Solving, the idea is instead that we're just going to estimate what the expected value is for the opponent's Subgames, for the opponent's actions for different Subgames, and use that information to determine the optimal strategy for the Subgame that we're in. Now, this works if your expected values are perfect, but if they're not perfect you're obviously not going | 1,504 | 1,521 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1504s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | to compute an exact Nash equilibrium. So, it turns out that there's room for improvement here. By the way, this idea has been around for awhile. It's was first introduced in 2014. It was never really used in practice because it didn't actually give you good results in practice. Because you don't have perfect estimates. But what we came up with, is a way to dramatically improve | 1,521 | 1,541 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1521s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | the performance without giving up any theoretical guarantees. With this thing called Reach Subgame Solving. So, here's an example of how this works. This is going to get a little tricky, so if you have any questions in the next few slides please let me know. So, let's say that we have this slightly larger game now. It's still basically the same structure, there's a coin flip that only player one observes. | 1,541 | 1,562 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1541s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Player one takes a sequence of actions, they eventually end up in this choice between selling the coin or playing, choosing play. Now, if they choose play, player two has to guess how the coin landed. Well, let's say your estimates are off in this game. Let's say we estimate that for choosing Sell, they will get an expected value of minus one regardless of which state they're in. | 1,562 | 1,581 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1562s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Well, the best that we can do is just guess 50-50 between heads and tails and guarantee that they get just an expected value zero, for choosing play. But maybe we can use information about the earlier actions to improve upon this. So, maybe there is this earlier action that player one could have chosen, if the coin landed heads, where they could have gotten expected value of 0.5. | 1,581 | 1,604 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1581s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Well, that means that in the Nash equilibrium, they would choose that action and get expected value of 0.5, and in the other case, they would come down here and choose play and get it fixed value of zero. So, they're getting an average of 0.25 in this game. But we can now shift our strategy as player two, to ensure we get tails more often, which guarantees that player one now | 1,604 | 1,624 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1604s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | gets negative 0.5 in this case. In the heads case that means they will get to 0.5 for choosing play, but that doesn't really matter because they're already getting 0.5 for this earlier deviate action. So, we're not really giving up anything in this situation, we're just making ourselves better off. Because they would never gets to the situation where they would choose the 0.5 anyway. | 1,624 | 1,644 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1624s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | This seems really intuitive but there's a problem with this, which is really subtle. I'm going to have to go to a bigger game, which is going to get even more complicated to really illustrate it. So, here is this bigger game. It's still pretty similar, that a coin that lands heads or tails with 50-50 probability. Player one in both cases now, let's say has this deviate action. | 1,644 | 1,663 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1644s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | In the heads case, they can get 0.5, and at tails case, they get minus 0.5. Or they can choose to continue, in which case we run into this chance node. This chance node is public. It just leads to two different Subgames, so both players observe the outcome of this chance node. It just leads to see different situations that are strategically identical. It's an irrelevant chance node, but it is a chance node. | 1,663 | 1,686 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1663s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Then after this chance node, player one let's say, chooses play and we estimate the expected value of them choosing play is now zero. So, let's say, we were player two in this game, we observe player one choose play. Which means that we are in one of these two different situations. Either the coin landed heads, they choose to continue and let's say we observed that the chance node end up going left, | 1,686 | 1,711 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1686s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and then they chose play. Or the coin landed tails, player one chose to continue. We observe the chance node going left and they choose play. So, we're in either this situation or this situation. Well, we observed that they have this deviate action of where they could've gotten expected value 0.5, if the coin landed heads. So, maybe we would say, we say, okay, well, | 1,711 | 1,736 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1711s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | we can increase the expected value for this action to one and lower it to minus one in this case, for example, by always guessing tails. That is okay because since this situation is only encountered 50 percent of the time, the expected value for this action is now just 0.5, and so that matches the deviant actions, so we're not giving up anything. Does anybody see the problem with this? All right. | 1,736 | 1,761 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1736s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | The problem is, if that chance node had gone the other way, if it had gone right, we would apply this same exact reasoning. We would say, okay, well, we can increase this expected value to one, because we're all encountering the situation half the time, so this expected value goes up to 0.5, and now the opponent is getting expected value zero, we're not giving up anything. | 1,761 | 1,782 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1761s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | But if we apply this reasoning regardless of which way this chance node goes, then what that means is our strategy is to always guess tails in both situations. So, in reality, it means that the expected value in this case is one and in this case is one, which means that the expected value is actually one, it's not 0.5. So, now player one could be better off by choosing to | 1,782 | 1,804 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1782s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | continue instead of choosing this deviate action. So, what this illustrates is that when you are doing this Subgame solving, you're doing this real-time reasoning, you can't look at the expected values of what we call the Blueprint Strategy, the pre-computed strategy. You have to think about what the expected values would have been if we had entered that Subgame and | 1,804 | 1,824 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1804s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | applied Subgame solving there too. So, that makes things that way more complicated. But fortunately, with Reach subgame solving, by the way, two prior papers had actually discussed this idea of, okay, we're encountering this situation, let's just increase the expected value for here, because they could have gotten an expected value earlier on and missed this problem that you have to consider | 1,824 | 1,848 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1824s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | about all the subgames that people could end up in. So, two prior papers published about this and they both got it wrong, and our paper, NIPS 2017 recognized this problem and actually came up with a fix that allows you to do this Reach subgame solving, while still guaranteeing that the points, your exploitability is not going to go up. The basic idea is to just only increase | 1,848 | 1,870 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1848s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | the expected value for both of these situations by 0.5. The actual details get a little bit more complicated, but the aren't too important for this talk. But the idea is you just increase the expected values by less depending on how many subgames they could end up in. You have question? >> Well, I was just wondering, I know this is really simple thing, you can't hold it. | 1,870 | 1,890 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1870s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | You don't think if it's just wrong versus this weird like if you only increase the values for the left of the public chance node. >> Yeah, so let's see where the situation- >> You set those first to explain it? >> Yeah. >> It seems like this is still correct. It's just weird because you're saying if nature flips a coin heads, then I'm going to do this weird reaction, | 1,890 | 1,911 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1890s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and if it's tails, then I'm not. >> So, I'll say this. If you were actually only increasing the expected value to one in this situation, and keeping the expected value at zero in this situation, that's totally fine. >> Okay. >> But you have to think about what would have happened. Imagine this from player one's perspective. If we would increase the expected value to one in | 1,911 | 1,931 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1911s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | this situation because this chance node went left, and we would have increased this expected value to one if this chance node are gone, right, Then what player one is thinking is that if they're in this situation they're thinking that, if I choose this action, regardless of which way this chance node goes, I'm getting expected value of one. >> Yeah, yeah. If our algorithms actually did. | 1,931 | 1,949 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1931s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | >> Yeah. So, that's what I'm saying is that, you have to think about what your algorithm would have done in all these other situations that didn't come up as player two, yeah. >> Okay. >> Okay. So, that's Reach subgame solving. Yeah, so the idea is for off path actions, we have to consider how we would have applied subgame solving and all these other situations that didn't come up. | 1,949 | 1,971 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1949s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | We have a solution for it, which is basically to split that what we call slack among the different subgames. We have a theorem that says, "Reach subgame solving will not increase the exploitability of a safe subgame solving's technique." If there is, these earlier actions where the opponent could have chosen a higher expected value, then it will actually improve performance | 1,971 | 1,991 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1971s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | relative to traditional subgame solving. In terms of actual, yes. >> [inaudible]. >> Yeah. >> Then you'll have to know the expected values for the subgames that are on the path from there. >> That's correct. So, you look at all the path, yeah, yes. You look at all the situations where the opponent could have gone off path. >> Yeah. >> You have to know the fixed values for those. Yeah. | 1,991 | 2,016 | https://www.youtube.com/watch?v=McV4a6umbAY&t=1991s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | >> I understand that these are values you put. So, is it correct when you're learning? So, it seems that you're allowed to do the updating some of these expected values, but then you are making this per all [inaudible]. >> Yes, so maybe I should have clarified this earlier. So, I'm assuming that we're basically run an algorithm that approximates a Nash equilibrium for the entire game, | 2,016 | 2,036 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2016s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | and that's where these expected values are coming from. So, we have this a rough approximation of what the Nash equilibrium is for the entire game, and that's giving us expected values for all these different actions, but they're not perfect. It's like with AlphaZero for example. AlphaZero gives you policy and values for all the different states that you might be in, | 2,036 | 2,053 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2036s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | but that's obviously not perfect and you can improve upon it by doing Monte-Carlo tree search in real-time. >> What do you mean formally by the safe technique to exploitability. So, you assume that [inaudible] is off by a certain fixed data? >> That's a great question. So, by safe subgames solving, I mean that there is some exploitability, our strategy, this pre-computed strategy that | 2,053 | 2,074 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2053s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | we have is exploitable by some amount. >> Assuming that all of these are correct or they have-? >> Well, I'm just saying that we've run this. Let's just say we've run a traditional reinforcement learning algorithm on the entire game, no real-time playing, just pre-computed strategy, that strategy that we have now is exploitable by some amount. I am saying that we would like to improve upon | 2,074 | 2,097 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2074s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | this in practice by doing real-time planning. But we want to guarantee that by doing real-time planning, we're at least not going to increase the exploitability of our strategy relative to what we had before. Now, in practice, it ends up being way lower exploitability, but we want to guarantee. We can't really guarantee that it's going to decrease in most situations, | 2,097 | 2,116 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2097s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | but we want at least guarantee that's not going to increase. So, that is what I mean by safe subgame solving. >> The purple like estimates from your pre-computed suboptimal value function? >> Yeah, so those are the values that we've estimated based on our prec-omputed strategy for the game. >> We can use those to compute the red basically? >> Yeah. >> Okay. >> So, the red is the real-time planning expected values. | 2,116 | 2,144 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2116s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | >> So, what's the right procedure? >> For time reasons, I decided to not really talk about how we're actually doing all this computation of the strategy. We use something called counterfactual rep minimization, which converges to an approximate solution and one over square root T time. So, if you do T iterations, you will get within one over square root T of | 2,144 | 2,167 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2144s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | the Nash equilibrium. Okay. >> Like in terms of the numbers things then. >> It is also, yes. So, it's linear in the number of information sets. >> So, like terabytes? >> Well, okay. So, with the broadest, we actually used about several terabytes of data and we used about millions of core hours of computation time. >> In real-time? >> In real time, no. In real time, it was lower. | 2,167 | 2,196 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2167s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | >> [inaudible] . >> So, that was for the pre-computed strategy. For real time, it ended up being we used about 1,000 cores, so about 50 nodes, and the memory is actually really small. It was probably less than 100 megabytes. We all actually figured out how to improve upon this massively, which I'll get to in a little bit. >> Is it a 100 like per core or per? | 2,196 | 2,221 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2196s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | >> No, it's the whole thing, 100 megabytes for the whole thing. The actual game, when you're solving from the turn onwards, like third betting rounds at the end of the game, the actual size of the game is pretty small, but because you have to compute a solution equilibrium for it, it takes a lot of computational power. >> So, was there a limit on how much time you have to make a decision? | 2,221 | 2,242 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2221s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | >> Yeah, we ended up doing it in less than 20 seconds or so. There wasn't like an official time limit, but we gave them some guidelines on how long it would take on average. We also didn't get the humans the time on it. So, if they wanted to take 10 minutes for a decision then that was fine with us. I will also, when we're thinking about the time on the thing. | 2,242 | 2,260 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2242s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | So, one of the interesting challenges of poker is that, you don't want to give it away timing tells, right? So, if it takes you two seconds to make a decision, then the opponent might think you have a really easy decision whereas, if you take two minutes, and it might be a difficult decision, they can figure out what hand you have. So, if you're playing, if you | 2,260 | 2,277 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2260s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | look at the World Series of Poker, it gets really annoying because, at the final table, they all take the same amount of time for every single decision. So, they take like two minutes for every single decision, even if it's a really trivial one. We didn't want the humans to have to do this because it would've taken forever and would pissed them off, would have pissed us off, so we told them flat | 2,277 | 2,293 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2277s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | out that the bot is not going to look at timing tells. So, if they took two seconds to make a decision, that's totally fine, we won't change anything. But we can't make them also do that for the bot, rather like if the bot took two seconds versus two minutes, they would pick up on that and they can't not pick up on that, right? So, we had to make the bot take the same amount of | 2,293 | 2,310 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2293s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | time for every single decision you made to prevent that. So, that's also why it ends up taking longer to do this thing. There's a lot of decisions that are easy, but we can't make that obvious. All right. So, experiments on medium-size games. So, it turns out that our reach subgame solving technique that I just described, that's about three times, it's about three times less exploitable. | 2,310 | 2,334 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2310s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Then, prior, safe subgame solving techniques, and nested subgame solving, this idea of applying subgame solving repeatedly as you go down the game tree. That is 12 times less exploitable than the prior state of the art, which is to just say, well, if the guy bet $60, and we have in our precomputed solution, a strategy for if he had bet $50, then we'll round it, and treat it | 2,334 | 2,355 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2334s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | as if you had bet $50 instead. That was the previous state of the art. So, this is 12 times less exploitable than that in Heads-up No-Limit Texas Hold'em. Sorry, in smaller versions of Heads up No-limit Texas Hold'em. Okay. So, that is one reason for why imperfect information games are hard. There is a second reason that I wanted to get to you, and I think I still have time to do it. | 2,355 | 2,377 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2355s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | This is more recent research. The second reason is that states don't have well defined values in imperfect-information games. So, let me show you what I mean here. In a perfect-information game, and it's single agent settings, if you take smashing, your opponent takes an action, you find yourself in a particular decision point is particularly subgame. You don't solve to the end of that subgame. | 2,377 | 2,398 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2377s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | Right? You do what's called depth limited reasoning. So, the remainder of the game is too large, so you come up with a strategy for the next several actions. Then, once you get to a certain depth limit, you say,okay, I've looked far enough, I'm just going to substitute a value for this leaf node, and say the value of this arrangement of pieces on the board looks like player one, | 2,398 | 2,420 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2398s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker | |
McV4a6umbAY | white wins with 60 percent probability. So, you assign a value to that state, and then you solve the depth limited subgame using those values at the leaf nodes. It turns out that this does not work in imperfect-information games. I can give you a really simple example of why. This is a game that I called Rock-Paper-Scissors+, is exactly like rock-paper-scissors, | 2,420 | 2,441 | https://www.youtube.com/watch?v=McV4a6umbAY&t=2420s | AI for Imperfect-Information Games: Beating Top Humans in No-Limit Poker |
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