Sam Ganzfried

AAAI Conference 2019 Conference Paper

Predicting Hurricane Trajectories Using a Recurrent Neural Network

• Sheila Alemany
• Jonathan Beltran
• Adrian Perez
• Sam Ganzfried

Hurricanes are cyclones circulating about a defined center whose closed wind speeds exceed 75 mph originating over tropical and subtropical waters. At landfall, hurricanes can result in severe disasters. The accuracy of predicting their trajectory paths is critical to reduce economic loss and save human lives. Given the complexity and nonlinearity of weather data, a recurrent neural network (RNN) could be beneficial in modeling hurricane behavior. We propose the application of a fully connected RNN to predict the trajectory of hurricanes. We employed the RNN over a fine grid to reduce typical truncation errors. We utilized their latitude, longitude, wind speed, and pressure publicly provided by the National Hurricane Center (NHC) to predict the trajectory of a hurricane at 6-hour intervals. Results show that this proposed technique is competitive to methods currently employed by the NHC and can predict up to approximately 120 hours of hurricane path.

AAAI Conference 2015 Conference Paper

Tartanian7: A Champion Two-Player No-Limit Texas Hold’em Poker-Playing Program

• Noam Brown
• Sam Ganzfried
• Tuomas Sandholm

AAAI Conference 2014 Conference Paper

Potential-Aware Imperfect-Recall Abstraction with Earth Mover’s Distance in Imperfect-Information Games

• Sam Ganzfried
• Tuomas Sandholm

There is often a large disparity between the size of a game we wish to solve and the size of the largest instances solvable by the best algorithms; for example, a popular variant of poker has about 10165 nodes in its game tree, while the currently best approximate equilibrium-finding algorithms scale to games with around 1012 nodes. In order to approximate equilibrium strategies in these games, the leading approach is to create a sufficiently small strategic approximation of the full game, called an abstraction, and to solve that smaller game instead. The leading abstraction algorithm for imperfect-information games generates abstractions that have imperfect recall and are distribution aware, using k-means with the earth mover’s distance metric to cluster similar states together. A distribution-aware abstraction groups states together at a given round if their full distributions over future strength are similar (as opposed to, for example, just the expectation of their strength). The leading algorithm considers distributions over future strength at the final round of the game. However, one might benefit by considering the trajectory of distributions over strength in all future rounds, not just the final round. An abstraction algorithm that takes all future rounds into account is called potential aware. We present the first algorithm for computing potential-aware imperfectrecall abstractions using earth mover’s distance. Experiments on no-limit Texas Hold’em show that our algorithm improves performance over the previously best approach.

IJCAI Conference 2013 Conference Paper

Action Translation in Extensive-Form Games with Large Action Spaces: Axioms, Paradoxes, and the Pseudo-Harmonic Mapping

• Sam Ganzfried
• Tuomas Sandholm

When solving extensive-form games with large action spaces, typically significant abstraction is needed to make the problem manageable from a modeling or computational perspective. When this occurs, a procedure is needed to interpret actions of the opponent that fall outside of our abstraction (by mapping them to actions in our abstraction). This is called an action translation mapping. Prior action translation mappings have been based on heuristics without theoretical justification. We show that the prior mappings are highly exploitable and that most of them violate certain natural desiderata. We present a new mapping that satisfies these desiderata and has significantly lower exploitability than the prior mappings. Furthermore, we observe that the cost of this worst-case performance benefit (low exploitability) is not high in practice; our mapping performs competitively with the prior mappings against no-limit Texas Hold’em agents submitted to the 2012 Annual Computer Poker Competition. We also observe several paradoxes that can arise when performing action abstraction and translation; for example, we show that it is possible to improve performance by including suboptimal actions in our abstraction and excluding optimal actions.

AAMAS Conference 2012 Conference Paper

Strategy Purification and Thresholding: Effective Non-Equilibrium Approaches for Playing Large Games

• Sam Ganzfried
• Tuomas Sandholm
• Kevin Waugh

There has been significant recent interest in computing effective strategies for playing large imperfect-information games. Much prior work involves computing an approximate equilibrium strategy in a smaller abstract game, then playing this strategy in the full game (with the hope that it also well approximates an equilibrium in the full game). In this paper, we present a family of modifications to this approach that work by constructing non-equilibrium strategies in the abstract game, which are then played in the full game. Our new procedures, called \emph{purification} and \emph{thresholding}, modify the action probabilities of an abstract equilibrium by preferring the higher-probability actions. Using a variety of domains, we show that these approaches lead to significantly stronger play than the standard equilibrium approach. As one example, our program that uses purification came in first place in the two-player no-limit Texas Hold'em total bankroll division of the 2010 Annual Computer Poker Competition. Surprisingly, we also show that purification significantly improves performance (against the full equilibrium strategy) in random 4 x 4 matrix games using random 3 x 3 abstractions. We present several additional results (both theoretical and empirical). Overall, one can view these approaches as ways of achieving robustness against overfitting one's strategy to one's lossy abstraction. Perhaps surprisingly, the performance gains do not necessarily come at the expense of worst-case exploitability.

AAMAS Conference 2011 Conference Paper

Game Theory-Based Opponent Modeling in Large Imperfect-Information Games

• Sam Ganzfried
• Tuomas Sandholm

We develop an algorithm for opponent modeling in large extensive-form games of imperfect information. It works by observing the opponent's action frequencies and building an opponent model by combining information from a precomputed equilibrium strategy with the observations. It then computes and plays a best response to this opponent model; the opponent model and best response are both updated continually in real time. The approach combines game-theoretic reasoning and pure opponent modeling, yielding a hybrid that can effectively exploit opponents after only a small number of interactions. Unlike prior opponent modeling approaches, ours is fundamentally game theoretic and takes advantage of recent algorithms for automated abstraction and equilibrium computation rather than relying on domain-specific prior distributions, historical data, or a handcrafted set of features. Experiments show that our algorithm leads to significantly higher win rates (than an approximate-equilibrium strategy) against several opponents in limit Texas Hold'em - the most studied imperfect-information game in computer science - including competitors from recent AAAI computer poker competitions.

AAMAS Conference 2011 Conference Paper

Strategy Purification

• Sam Ganzfried
• Tuomas Sandholm
• Kevin Waugh

There has been significant recent interest in computing good strategies for large games. Most prior work involves computing an approximate equilibrium strategy in a smaller abstract game, then playing this strategy in the full game. In this paper, we present a modification of this approach that works by constructing a deterministic strategy in the full game from the solution to the abstract game; we refer to this procedure as purification. We show that purification, and its generalization which we call thresholding, lead to significantly stronger play than the standard approach in a wide variety of experimental domains. One can view these approaches as ways of achieving robustness against one's own lossy abstraction.

AAMAS Conference 2010 Conference Paper

Computing Equilibria by Incorporating Qualitative Models

• Sam Ganzfried
• Tuomas Sandholm

We present a new procedure for solving large games of imperfect information. Our approach involves - somewhat counterintuitively - solving an infinite approximation of the original game, then mapping the equilibrium to a strategy profile in the original game. Our main algorithm exploits some qualitative model of equilibrium structure as an additional input to find an equilibrium in continuous games. We prove that our approach is correct even if given a set of qualitative models (satisfying a technical property) of which only some are accurate. We compute equilibria in several classes of games for which no prior algorithms have been developed. In the course of our analysis, we also develop the first mixed-integer programming formulations for computing an epsilon-equilibrium in general multiplayer normal and extensive-form games based on the extension of our initial algorithm to the multiplayer setting, which may be of independent interest. Experiments suggest that our approach can outperform the prior state of the art, abstraction-based approaches. In addition, we demonstrate the effectiveness of our main algorithm on a subgame of limit Texas hold'em - the most studied imperfect-information game in computer science.

IJCAI Conference 2009 Conference Paper

• Sam Ganzfried
• Tuomas Sandholm

Computing a Nash equilibrium in multiplayer stochastic games is a notoriously difficult problem. Prior algorithms have been proven to converge in extremely limited settings and have only been tested on small problems. In contrast, we recently presented an algorithm for computing approximate jam/fold equilibrium strategies in a three-player nolimit Texas hold’em tournament—a very large realworld stochastic game of imperfect information [5]. In this paper we show that it is possible for that algorithm to converge to a non-equilibrium strategy profile. However, we develop an ex post procedure that determines exactly how much each player can gain by deviating from his strategy and confirm that the strategies computed in that paper actually do constitute an -equilibrium for a very small (0. 5% of the tournament entry fee). Next, we develop several new algorithms for computing a Nash equilibrium in multiplayer stochastic games (with perfect or imperfect information) which can provably never converge to a non-equilibrium. Experiments show that one of these algorithms outperforms the original algorithm on the same poker tournament. In short, we present the first algorithms for provably computing an -equilibrium of a large stochastic game for small. Finally, we present an efficient algorithm that minimizes external regret in both the perfect and imperfect information cases.

AAMAS Conference 2008 Conference Paper

Computing an Approximate Jam/Fold Equilibrium for 3-player No-Limit Texas Hold'em Tournaments

• Sam Ganzfried
• Tuomas Sandholm

A recent paper computes near-optimal strategies for twoplayer no-limit Texas hold’em tournaments; however, the techniques used are unable to compute equilibrium strategies for tournaments with more than two players. Motivated by the widespread popularity of multiplayer tournaments and the observation that jam/fold strategies are nearoptimal in the two player case, we develop an algorithm that computes approximate jam/fold equilibrium strategies in tournaments with three — and potentially even more — players. Our algorithm combines an extension of fictitious play to imperfect information games, an algorithm similar to value iteration for solving stochastic games, and a heuristic from the poker community known as the Independent Chip Model which we use as an initialization. Several ways of exploiting suit symmetries and the use of custom indexing schemes made the approach computationally feasible. Aside from the initialization and the restriction to jam/fold strategies, our high level algorithm makes no poker-specific assumptions and thus also applies to other multiplayer stochastic games of imperfect information.