Ganzfried, Sam


Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game

arXiv.org Artificial Intelligence

Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in two-player zero-sum games, but no guarantees in non-zero-sum games or in games with more than two players. We describe an agent that is able to defeat a variety of realistic opponents using an exact Nash equilibrium strategy in a 3-player imperfect-information game. This shows that, despite a lack of theoretical guarantees, agents based on Nash equilibrium strategies can be successful in multiplayer games after all.


Predicting Hurricane Trajectories using a Recurrent Neural Network

arXiv.org Machine Learning

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 (NOAA) to predict the trajectory of a hurricane at 6-hour intervals.


Bayesian Opponent Exploitation in Imperfect-Information Games

AAAI Conferences

Two fundamental problems in computational game theory are computing a Nash equilibrium and learning to exploit opponents given observations of their play (opponent exploitation). The latter is perhaps even more important than the former: Nash equilibrium does not have a compelling theoretical justification in game classes other than two-player zero-sum, and for all games one can potentially do better by exploiting perceived weaknesses of the opponent than by following a static equilibrium strategy throughout the match. The natural setting for opponent exploitation is the Bayesian setting where we have a prior model that is integrated with observations to create a posterior opponent model that we respond to. The most natural, and a well-studied prior distribution is the Dirichlet distribution. An exact polynomial-time algorithm is known for best-responding to the posterior distribution for an opponent assuming a Dirichlet prior with multinomial sampling in normal-form games; however, for imperfect-information games the best known algorithm is based on approximating an infinite integral without theoretical guarantees. We present the first exact algorithm for a natural class of imperfect-information games. We demonstrate that our algorithm runs quickly in practice and outperforms the best prior approaches. We also present an algorithm for the uniform prior setting.


Optimal Number of Choices in Rating Contexts

arXiv.org Artificial Intelligence

In many settings people must give numerical scores to entities from a small discrete set. For instance, rating physical attractiveness from 1--5 on dating sites, or papers from 1--10 for conference reviewing. We study the problem of understanding when using a different number of options is optimal. For concreteness we assume the true underlying scores are integers from 1--100. We consider the case when scores are uniform random and Gaussian. We study when using 2, 3, 4, 5, and 10 options is optimal in these models. One may expect that using more options would always improve performance in this model, but we show that this is not necessarily the case, and that using fewer choices---even just two---can surprisingly be optimal in certain situations. While in theory for this setting it would be optimal to use all 100 options, in practice this is prohibitive, and it is preferable to utilize a smaller number of options due to humans' limited computational resources. Our results suggest that using a smaller number of options than is typical could be optimal in certain situations. This would have many potential applications, as settings requiring entities to be ranked by humans are ubiquitous.



Bayesian Opponent Exploitation in Imperfect-Information Games

arXiv.org Artificial Intelligence

Two fundamental problems in computational game theory are computing a Nash equilibrium and learning to exploit opponents given observations of their play (opponent exploitation). The latter is perhaps even more important than the former: Nash equilibrium does not have a compelling theoretical justification in game classes other than two-player zero-sum, and for all games one can potentially do better by exploiting perceived weaknesses of the opponent than by following a static equilibrium strategy throughout the match. The natural setting for opponent exploitation is the Bayesian setting where we have a prior model that is integrated with observations to create a posterior opponent model that we respond to. The most natural, and a well-studied prior distribution is the Dirichlet distribution. An exact polynomial-time algorithm is known for best-responding to the posterior distribution for an opponent assuming a Dirichlet prior with multinomial sampling in normal-form games; however, for imperfect-information games the best known algorithm is based on approximating an infinite integral without theoretical guarantees. We present the first exact algorithm for a natural class of imperfect-information games. We demonstrate that our algorithm runs quickly in practice and outperforms the best prior approaches. We also present an algorithm for the uniform prior setting.


Learning Human-Understandable Strategies

AAAI Conferences

Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In many situations, we would like to compute strategies that can actually be implemented by humans, who may have computational limitations and may only be able to remember a small number of features or components of the strategies that have been computed. We study poker games where private information distributions can be arbitrary. We create a large training set of game instances and solutions, by randomly selecting the private information probabilities, and present algorithms that learn from the training instances in order to perform well in games with unseen information distributions. One approach first clusters the training points into a small number of clusters and then creates a small decision tree based on the cluster centers. This approach produces low test error and could be easily implemented by humans since it only requires memorizing a small number of "if-then" rules.


Computing Strong Game-Theoretic Strategies in Jotto

arXiv.org Artificial Intelligence

We develop a new approach that computes approximate equilibrium strategies in Jotto, a popular word game. Jotto is an extremely large two-player game of imperfect information; its game tree has many orders of magnitude more states than games previously studied, including no-limit Texas hold 'em. To address the fact that the game is so large, we propose a novel strategy representation called oracular form, in which we do not explicitly represent a strategy, but rather appeal to an oracle that quickly outputs a sample move from the strategy's distribution. Our overall approach is based on an extension of the fictitious play algorithm to this oracular setting. We demonstrate the superiority of our computed strategies over the strategies computed by a benchmark algorithm, both in terms of head-to-head and worst-case performance.


Reports on the 2015 AAAI Workshop Program

AI Magazine

AAAI's 2015 Workshop Program was held Sunday and Monday, January 25–26, 2015 at the Hyatt Regency Austin Hotel in Austion, Texas, USA. The AAAI-15 workshop program included 15 workshops covering a wide range of topics in artificial intelligence. Most workshops were held on a single day. The titles of the workshops included AI and Ethics, AI for Cities, AI for Transportation: Advice, Interactivity and Actor Modeling, Algorithm Configuration, Artificial Intelligence Applied to Assistive Technologies and Smart Environments, Beyond the Turing Test, Computational Sustainability, Computer Poker and Imperfect Information, Incentive and Trust in E-Communities, Multiagent Interaction without Prior Coordination, Planning, Search, and Optimization, Scholarly Big Data: AI Perspectives, Challenges, and Ideas, Trajectory-Based Behaviour Analytics, World Wide Web and Public Health Intelligence, Knowledge, Skill, and Behavior Transfer in Autonomous Robots, and Learning for General Competency in Video Games.


Reports on the 2015 AAAI Workshop Program

AI Magazine

AAAI's 2015 Workshop Program was held Sunday and Monday, January 25–26, 2015 at the Hyatt Regency Austin Hotel in Austion, Texas, USA. The AAAI-15 workshop program included 15 workshops covering a wide range of topics in artificial intelligence. Most workshops were held on a single day. The titles of the workshops included AI and Ethics, AI for Cities, AI for Transportation: Advice, Interactivity and Actor Modeling, Algorithm Configuration, Artificial Intelligence Applied to Assistive Technologies and Smart Environments, Beyond the Turing Test, Computational Sustainability, Computer Poker and Imperfect Information, Incentive and Trust in E-Communities, Multiagent Interaction without Prior Coordination, Planning, Search, and Optimization, Scholarly Big Data: AI Perspectives, Challenges, and Ideas, Trajectory-Based Behaviour Analytics, World Wide Web and Public Health Intelligence, Knowledge, Skill, and Behavior Transfer in Autonomous Robots, and Learning for General Competency in Video Games.