Safe Opponent Exploitation For Epsilon Equilibrium Strategies

In safe opponent exploitation players hope to exploit their opponents' potentially sub-optimal strategies while guaranteeing at least the value of the game in expectation for themselves. Safe opponent exploitation algorithms have been successfully applied to small instances of two-player zero-sum imperfect information games, where Nash equilibrium strategies are typically known in advance. Current methods available to compute these strategies are however not scalable to desirable large domains of imperfect information such as No-Limit Texas Hold 'em (NLHE) poker, where successful agents rely on game abstractions in order to compute an equilibrium strategy approximation. This paper will extend the concept of safe opponent exploitation by introducing prime-safe opponent exploitation, in which we redefine the value of the game of a player to be the worst-case payoff their strategy could be susceptible to. This allows weaker epsilon equilibrium strategies to benefit from utilising a form of opponent exploitation with our revised value of the game, still allowing for a practical game-theoretical guaranteed lower-bound. We demonstrate the empirical advantages of our generalisation when applied to the main safe opponent exploitation algorithms

Applying machine learning techniques to an imperfect information game

The game of poker presents a challenging game to Artificial Intelligence researchers because it is a complex asymmetric information game. In such games, a player can improve his performance by inferring the private information held by the other players from their prior actions. A novel connectionist structure was designed to play a version of poker (multi-player limit Hold‟em). This allows simple reinforcement learning techniques to be used which previously not been considered for the game of multi-player hold‟em. A related hidden Markov model was designed to be fitted to records of poker play without using any private information. Belief vectors generated by this model provide a more convenient and flexible representation of an opponent‟s action history than alternative approaches. The structure was tested in two settings. Firstly self-play simulation was used to generate an approximation to a Nash equilibrium strategy. A related, but slower, rollout strategy that uses Monte-Carlo samples was used to evaluate the performance. Secondly the structure was used to model and hence exploit a population of opponents within a relatively small number of games. When and how to adapt quickly to new opponents are open questions in poker AI research. A opponent model with a small number of discrete types is used to identify the largest differences in strategy between members of the population. A commercial software package (Poker Academy) was used to provide a population of sophisticated opponents to test against. A series of experiments was conducted to compare adaptive and static systems. All systems showed positive results but surprisingly the adaptive systems did not show a significant improvement over similar static systems. The possible reasons for this result are discussed. This work formed the basis of a series of entries to the computer poker competition hosted at the annual conferences of the Association for the Advancement of Artificial Intelligence (AAAI). Its best rankings were 3rd in the 2006 6-player limit hold‟em competition and 2nd in the 2008 3-player limit hold‟em competition

Model-Free Online Learning in Unknown Sequential Decision Making Problems and Games

Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR) are currently the practical state of the art for computing a Nash equilibrium. Most regret-minimization algorithms for tree-form sequential decision making, including CFR, require (i) an exact model of the player's decision nodes, observation nodes, and how they are linked, and (ii) full knowledge, at all times t, about the payoffs -- even in parts of the decision space that are not encountered at time t. Recently, there has been growing interest towards relaxing some of those restrictions and making regret minimization applicable to settings for which reinforcement learning methods have traditionally been used -- for example, those in which only black-box access to the environment is available. We give the first, to our knowledge, regret-minimization algorithm that guarantees sublinear regret with high probability even when requirement (i) -- and thus also (ii) -- is dropped. We formalize an online learning setting in which the strategy space is not known to the agent and gets revealed incrementally whenever the agent encounters new decision points. We give an efficient algorithm that achieves $O(T^{3/4})$ regret with high probability for that setting, even when the agent faces an adversarial environment. Our experiments show it significantly outperforms the prior algorithms for the problem, which do not have such guarantees. It can be used in any application for which regret minimization is useful: approximating Nash equilibrium or quantal response equilibrium, approximating coarse correlated equilibrium in multi-player games, learning a best response, learning safe opponent exploitation, and online play against an unknown opponent/environment.Comment: Full version. The body of the paper appeared in the proceedings of the AAAI 2021 conferenc

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Machine learning applied to the context of Poker

A combinação de princípios da teoria de jogo e metodologias de machine learning aplicados ao contexto de formular estratégias ótimas para jogos está a angariar interesse por parte de uma porção crescentemente significativa da comunidade científica, tornando-se o jogo do Poker num candidato de estudo popular devido à sua natureza de informação imperfeita. Avanços nesta área possuem vastas aplicações em cenários do mundo real, e a área de investigação de inteligência artificial demonstra que o interesse relativo a este objeto de estudo está longe de desaparecer, com investigadores do Facebook e Carnegie Mellon a apresentar, em 2019, o primeiro agente de jogo autónomo de Poker provado como ganhador num cenário com múltiplos jogadores, uma conquista relativamente à anterior especificação do estado da arte, que fora desenvolvida para jogos de apenas 2 jogadores. Este estudo pretende explorar as características de jogos estocásticos de informação imperfeita, recolhendo informação acerca dos avanços nas metodologias disponibilizados por parte de investigadores de forma a desenvolver um agente autónomo de jogo que se pretende inserir na classificação de "utility-maximizing decision-maker".The combination of game theory principles and machine learning methodologies applied to encountering optimal strategies for games is garnering interest from an increasing large portion of the scientific community, with the game of Poker being a popular study subject due to its imperfect information nature. Advancements in this area have a wide array of applications in real-world scenarios, and the field of artificial intelligent studies show that the interest regarding this object of study is yet to fade, with researchers from Facebook and Carnegie Mellon presenting, in 2019, the world’s first autonomous Poker playing agent that is proven to be profitable while confronting multiple players at a time, an achievement in relation to the previous state of the art specification, which was developed for two player games only. This study intends to explore the characteristics of stochastic games of imperfect information, gathering information regarding the advancements in methodologies made available by researchers in order to ultimately develop an autonomous agent intended to adhere to the classification of a utility-maximizing decision-maker

REX: Rapid Exploration and eXploitation for AI Agents

In this paper, we propose an enhanced approach for Rapid Exploration and eXploitation for AI Agents called REX. Existing AutoGPT-style techniques have inherent limitations, such as a heavy reliance on precise descriptions for decision-making, and the lack of a systematic approach to leverage try-and-fail procedures akin to traditional Reinforcement Learning (RL). REX introduces an additional layer of rewards and integrates concepts similar to Upper Confidence Bound (UCB) scores, leading to more robust and efficient AI agent performance. This approach has the advantage of enabling the utilization of offline behaviors from logs and allowing seamless integration with existing foundation models while it does not require any model fine-tuning. Through comparative analysis with existing methods such as Chain-of-Thoughts(CoT) and Reasoning viA Planning(RAP), REX-based methods demonstrate comparable performance and, in certain cases, even surpass the results achieved by these existing techniques. Notably, REX-based methods exhibit remarkable reductions in execution time, enhancing their practical applicability across a diverse set of scenarios

Reinforcement Learning from Self-Play in Imperfect-Information Games

This thesis investigates artificial agents learning to make strategic decisions in imperfect-information games. In particular, we introduce a novel approach to reinforcement learning from self-play. We introduce Smooth UCT, which combines the game-theoretic notion of fictitious play with Monte Carlo Tree Search (MCTS). Smooth UCT outperformed a classic MCTS method in several imperfect-information poker games and won three silver medals in the 2014 Annual Computer Poker Competition. We develop Extensive-Form Fictitious Play (XFP) that is entirely implemented in sequential strategies, thus extending this prominent game-theoretic model of learning to sequential games. XFP provides a principled foundation for self-play reinforcement learning in imperfect-information games. We introduce Fictitious Self-Play (FSP), a class of sample-based reinforcement learning algorithms that approximate XFP. We instantiate FSP with neuralnetwork function approximation and deep learning techniques, producing Neural FSP (NFSP). We demonstrate that (approximate) Nash equilibria and their representations (abstractions) can be learned using NFSP end to end, i.e. interfacing with the raw inputs and outputs of the domain. NFSP approached the performance of state-of-the-art, superhuman algorithms in Limit Texas Hold’em - an imperfect-information game at the absolute limit of tractability using massive computational resources. This is the first time that any reinforcement learning algorithm, learning solely from game outcomes without prior domain knowledge, achieved such a feat

Bandit Linear Optimization for Sequential Decision Making and Extensive-Form Games

Tree-form sequential decision making (TFSDM) extends classical one-shot decision making by modeling tree-form interactions between an agent and a potentially adversarial environment. It captures the online decision-making problems that each player faces in an extensive-form game, as well as Markov decision processes and partially-observable Markov decision processes where the agent conditions on observed history. Over the past decade, there has been considerable effort into designing online optimization methods for TFSDM. Virtually all of that work has been in the full-feedback setting, where the agent has access to counterfactuals, that is, information on what would have happened had the agent chosen a different action at any decision node. Little is known about the bandit setting, where that assumption is reversed (no counterfactual information is available), despite this latter setting being well understood for almost 20 years in one-shot decision making. In this paper, we give the first algorithm for the bandit linear optimization problem for TFSDM that offers both (i) linear-time iterations (in the size of the decision tree) and (ii) $O(\sqrt{T})$ cumulative regret in expectation compared to any fixed strategy, at all times $T$. This is made possible by new results that we derive, which may have independent uses as well: 1) geometry of the dilated entropy regularizer, 2) autocorrelation matrix of the natural sampling scheme for sequence-form strategies, 3) construction of an unbiased estimator for linear losses for sequence-form strategies, and 4) a refined regret analysis for mirror descent when using the dilated entropy regularizer.Comment: Full version. The body of the paper appeared in the proceedings of the AAAI 2021 conferenc