Daily Papers

Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn epsilon-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound mathcal{O}(H(A_{X}+B_{Y})/epsilon^2) on the required number of realizations to learn these strategies with high probability, where H is the length of the game, A_{X} and B_{Y} are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs mathcal{O}(H^2(A_{X}+B_{Y})/epsilon^2) realizations without this requirement by progressively adapting the regularization to the observations.

Unlike perfect information games, where all elements are known to every player, imperfect information games emulate the real-world complexities of decision-making under uncertain or incomplete information. GPT-4, the recent breakthrough in large language models (LLMs) trained on massive passive data, is notable for its knowledge retrieval and reasoning abilities. This paper delves into the applicability of GPT-4's learned knowledge for imperfect information games. To achieve this, we introduce Suspicion-Agent, an innovative agent that leverages GPT-4's capabilities for performing in imperfect information games. With proper prompt engineering to achieve different functions, Suspicion-Agent based on GPT-4 demonstrates remarkable adaptability across a range of imperfect information card games. Importantly, GPT-4 displays a strong high-order theory of mind (ToM) capacity, meaning it can understand others and intentionally impact others' behavior. Leveraging this, we design a planning strategy that enables GPT-4 to competently play against different opponents, adapting its gameplay style as needed, while requiring only the game rules and descriptions of observations as input. In the experiments, we qualitatively showcase the capabilities of Suspicion-Agent across three different imperfect information games and then quantitatively evaluate it in Leduc Hold'em. The results show that Suspicion-Agent can potentially outperform traditional algorithms designed for imperfect information games, without any specialized training or examples. In order to encourage and foster deeper insights within the community, we make our game-related data publicly available.

An imperfect-information game is a type of game with asymmetric information. It is more common in life than perfect-information game. Artificial intelligence (AI) in imperfect-information games, such like poker, has made considerable progress and success in recent years. The great success of superhuman poker AI, such as Libratus and Deepstack, attracts researchers to pay attention to poker research. However, the lack of open-source code limits the development of Texas hold'em AI to some extent. This article introduces DecisionHoldem, a high-level AI for heads-up no-limit Texas hold'em with safe depth-limited subgame solving by considering possible ranges of opponent's private hands to reduce the exploitability of the strategy. Experimental results show that DecisionHoldem defeats the strongest openly available agent in heads-up no-limit Texas hold'em poker, namely Slumbot, and a high-level reproduction of Deepstack, viz, Openstack, by more than 730 mbb/h (one-thousandth big blind per round) and 700 mbb/h. Moreover, we release the source codes and tools of DecisionHoldem to promote AI development in imperfect-information games.

We consider learning to play multiplayer imperfect-information games with simultaneous moves and large state-action spaces. Previous attempts to tackle such challenging games have largely focused on model-free learning methods, often requiring hundreds of years of experience to produce competitive agents. Our approach is based on model-based planning. We tackle the problem of partial observability by first building an (oracle) planner that has access to the full state of the environment and then distilling the knowledge of the oracle to a (follower) agent which is trained to play the imperfect-information game by imitating the oracle's choices. We experimentally show that planning with naive Monte Carlo tree search does not perform very well in large combinatorial action spaces. We therefore propose planning with a fixed-depth tree search and decoupled Thompson sampling for action selection. We show that the planner is able to discover efficient playing strategies in the games of Clash Royale and Pommerman and the follower policy successfully learns to implement them by training on a few hundred battles.

Test-time reasoning significantly enhances pre-trained AI agents' performance. However, it requires an explicit environment model, often unavailable or overly complex in real-world scenarios. While MuZero enables effective model learning for search in perfect information games, extending this paradigm to imperfect information games presents substantial challenges due to more nuanced look-ahead reasoning techniques and large number of states relevant for individual decisions. This paper introduces an algorithm LAMIR that learns an abstracted model of an imperfect information game directly from the agent-environment interaction. During test time, this trained model is used to perform look-ahead reasoning. The learned abstraction limits the size of each subgame to a manageable size, making theoretically principled look-ahead reasoning tractable even in games where previous methods could not scale. We empirically demonstrate that with sufficient capacity, LAMIR learns the exact underlying game structure, and with limited capacity, it still learns a valuable abstraction, which improves game playing performance of the pre-trained agents even in large games.

RLCard is an open-source toolkit for reinforcement learning research in card games. It supports various card environments with easy-to-use interfaces, including Blackjack, Leduc Hold'em, Texas Hold'em, UNO, Dou Dizhu and Mahjong. The goal of RLCard is to bridge reinforcement learning and imperfect information games, and push forward the research of reinforcement learning in domains with multiple agents, large state and action space, and sparse reward. In this paper, we provide an overview of the key components in RLCard, a discussion of the design principles, a brief introduction of the interfaces, and comprehensive evaluations of the environments. The codes and documents are available at https://github.com/datamllab/rlcard

Advances in intelligent game playing agents have led to successes in perfect information games like Go and imperfect information games like Poker. The Information Set Monte Carlo Tree Search (ISMCTS) family of algorithms outperforms previous algorithms using Monte Carlo methods in imperfect information games. In this paper, Single Observer Information Set Monte Carlo Tree Search (SO-ISMCTS) is applied to Secret Hitler, a popular social deduction board game that combines traditional hidden role mechanics with the randomness of a card deck. This combination leads to a more complex information model than the hidden role and card deck mechanics alone. It is shown in 10108 simulated games that SO-ISMCTS plays as well as simpler rule based agents, and demonstrates the potential of ISMCTS algorithms in complicated information set domains.

We study how to learn ε-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of episodes, denoted by T. Existing procedures suffer from high variance due to the use of importance sampling over sequences of actions (Steinberger et al., 2020; McAleer et al., 2022). To reduce this variance, we consider a fixed sampling approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a regularized loss. We show that this approach guarantees a convergence rate of mathcal{O}(T^{-1/2}) with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

OpenSpiel is a collection of environments and algorithms for research in general reinforcement learning and search/planning in games. OpenSpiel supports n-player (single- and multi- agent) zero-sum, cooperative and general-sum, one-shot and sequential, strictly turn-taking and simultaneous-move, perfect and imperfect information games, as well as traditional multiagent environments such as (partially- and fully- observable) grid worlds and social dilemmas. OpenSpiel also includes tools to analyze learning dynamics and other common evaluation metrics. This document serves both as an overview of the code base and an introduction to the terminology, core concepts, and algorithms across the fields of reinforcement learning, computational game theory, and search.

We study the problem of learning a Nash equilibrium (NE) in an imperfect information game (IIG) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular IIG under the perfect-recall assumption where the only feedback is realizations of the game (bandit feedback). In particular, the dynamic of the IIG is not known -- we can only access it by sampling or interacting with a game simulator. For this learning setting, we provide the Implicit Exploration Online Mirror Descent (IXOMD) algorithm. It is a model-free algorithm with a high-probability bound on the convergence rate to the NE of order 1/T where T is the number of played games. Moreover, IXOMD is computationally efficient as it needs to perform the updates only along the sampled trajectory.

The process of revising (or constructing) a policy at execution time -- known as decision-time planning -- has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading to superhuman performance in poker. However, these methods involve solving subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large. Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on solving subgames, but rather on update equivalence. In this update-equivalence framework, decision-time planning algorithms replicate the updates of last-iterate algorithms, which need not rely on public information. This facilitates scalability to games with large amounts of non-public information. Using this framework, we derive a provably sound search algorithm for fully cooperative games based on mirror descent and a search algorithm for adversarial games based on magnetic mirror descent. We validate the performance of these algorithms in cooperative and adversarial domains, notably in Hanabi, the standard benchmark for search in fully cooperative imperfect-information games. Here, our mirror descent approach exceeds or matches the performance of public information-based search while using two orders of magnitude less search time. This is the first instance of a non-public-information-based algorithm outperforming public-information-based approaches in a domain they have historically dominated.

Poker, also known as Texas Hold'em, has always been a typical research target within imperfect information games (IIGs). IIGs have long served as a measure of artificial intelligence (AI) development. Representative prior works, such as DeepStack and Libratus heavily rely on counterfactual regret minimization (CFR) to tackle heads-up no-limit Poker. However, it is challenging for subsequent researchers to learn CFR from previous models and apply it to other real-world applications due to the expensive computational cost of CFR iterations. Additionally, CFR is difficult to apply to multi-player games due to the exponential growth of the game tree size. In this work, we introduce PokerGPT, an end-to-end solver for playing Texas Hold'em with arbitrary number of players and gaining high win rates, established on a lightweight large language model (LLM). PokerGPT only requires simple textual information of Poker games for generating decision-making advice, thus guaranteeing the convenient interaction between AI and humans. We mainly transform a set of textual records acquired from real games into prompts, and use them to fine-tune a lightweight pre-trained LLM using reinforcement learning human feedback technique. To improve fine-tuning performance, we conduct prompt engineering on raw data, including filtering useful information, selecting behaviors of players with high win rates, and further processing them into textual instruction using multiple prompt engineering techniques. Through the experiments, we demonstrate that PokerGPT outperforms previous approaches in terms of win rate, model size, training time, and response speed, indicating the great potential of LLMs in solving IIGs.

For a two-player imperfect-information extensive-form game (IIEFG) with K time steps and a player action space of size U, the game tree complexity is U^{2K}, causing existing IIEFG solvers to struggle with large or infinite (U,K), e.g., differential games with continuous action spaces. To partially address this scalability challenge, we focus on an important class of 2p0s games where the informed player (P1) knows the payoff while the uninformed player (P2) only has a belief over the set of I possible payoffs. Such games encompass a wide range of scenarios in sports, defense, cybersecurity, and finance. We prove that under mild conditions, P1's (resp. P2's) equilibrium strategy at any infostate concentrates on at most I (resp. I+1) action prototypes. When Ill U, this equilibrium structure causes the game tree complexity to collapse to I^K for P1 when P2 plays pure best responses, and (I+1)^K for P2 in a dual game where P1 plays pure best responses. We then show that exploiting this structure in standard learning modes, i.e., model-free multiagent reinforcement learning and model predictive control, is straightforward, leading to significant improvements in learning accuracy and efficiency from SOTA IIEFG solvers. Our demonstration solves a 22-player football game (K=10, U=infty) where the attacking team has to strategically conceal their intention until a critical moment in order to exploit information advantage. Code is available at https://github.com/ghimiremukesh/cams/tree/iclr

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect-information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective to solving two-player zero-sum games and yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed.

We introduce a framework for translating game descriptions in natural language into extensive-form representations in game theory, leveraging Large Language Models (LLMs) and in-context learning. Given the varying levels of strategic complexity in games, such as perfect versus imperfect information, directly applying in-context learning would be insufficient. To address this, we introduce a two-stage framework with specialized modules to enhance in-context learning, enabling it to divide and conquer the problem effectively. In the first stage, we tackle the challenge of imperfect information by developing a module that identifies information sets along and the corresponding partial tree structure. With this information, the second stage leverages in-context learning alongside a self-debugging module to produce a complete extensive-form game tree represented using pygambit, the Python API of a recognized game-theoretic analysis tool called Gambit. Using this python representation enables the automation of tasks such as computing Nash equilibria directly from natural language descriptions. We evaluate the performance of the full framework, as well as its individual components, using various LLMs on games with different levels of strategic complexity. Our experimental results show that the framework significantly outperforms baseline models in generating accurate extensive-form games, with each module playing a critical role in its success.

Mahjong is a popular multi-player imperfect-information game developed in China in the late 19th-century, with some very challenging features for AI research. Sanma, being a 3-player variant of the Japanese Riichi Mahjong, possesses unique characteristics including fewer tiles and, consequently, a more aggressive playing style. It is thus challenging and of great research interest in its own right, but has not yet been explored. In this paper, we present Meowjong, an AI for Sanma using deep reinforcement learning. We define an informative and compact 2-dimensional data structure for encoding the observable information in a Sanma game. We pre-train 5 convolutional neural networks (CNNs) for Sanma's 5 actions -- discard, Pon, Kan, Kita and Riichi, and enhance the major action's model, namely the discard model, via self-play reinforcement learning using the Monte Carlo policy gradient method. Meowjong's models achieve test accuracies comparable with AIs for 4-player Mahjong through supervised learning, and gain a significant further enhancement from reinforcement learning. Being the first ever AI in Sanma, we claim that Meowjong stands as a state-of-the-art in this game.

When applied to question answering and other text generation tasks, language models (LMs) may be queried generatively (by sampling answers from their output distribution) or discriminatively (by using them to score or rank a set of candidate outputs). These procedures sometimes yield very different predictions. How do we reconcile mutually incompatible scoring procedures to obtain coherent LM predictions? We introduce a new, a training-free, game-theoretic procedure for language model decoding. Our approach casts language model decoding as a regularized imperfect-information sequential signaling game - which we term the CONSENSUS GAME - in which a GENERATOR seeks to communicate an abstract correctness parameter using natural language sentences to a DISCRIMINATOR. We develop computational procedures for finding approximate equilibria of this game, resulting in a decoding algorithm we call EQUILIBRIUM-RANKING. Applied to a large number of tasks (including reading comprehension, commonsense reasoning, mathematical problem-solving, and dialog), EQUILIBRIUM-RANKING consistently, and sometimes substantially, improves performance over existing LM decoding procedures - on multiple benchmarks, we observe that applying EQUILIBRIUM-RANKING to LLaMA-7B outperforms the much larger LLaMA-65B and PaLM-540B models. These results highlight the promise of game-theoretic tools for addressing fundamental challenges of truthfulness and consistency in LMs.

The generalization of decision-making agents encompasses two fundamental elements: learning from past experiences and reasoning in novel contexts. However, the predominant emphasis in most interactive environments is on learning, often at the expense of complexity in reasoning. In this paper, we introduce CivRealm, an environment inspired by the Civilization game. Civilization's profound alignment with human history and society necessitates sophisticated learning, while its ever-changing situations demand strong reasoning to generalize. Particularly, CivRealm sets up an imperfect-information general-sum game with a changing number of players; it presents a plethora of complex features, challenging the agent to deal with open-ended stochastic environments that require diplomacy and negotiation skills. Within CivRealm, we provide interfaces for two typical agent types: tensor-based agents that focus on learning, and language-based agents that emphasize reasoning. To catalyze further research, we present initial results for both paradigms. The canonical RL-based agents exhibit reasonable performance in mini-games, whereas both RL- and LLM-based agents struggle to make substantial progress in the full game. Overall, CivRealm stands as a unique learning and reasoning challenge for decision-making agents. The code is available at https://github.com/bigai-ai/civrealm.

This study evaluates Artificial Intelligence (AI) agents for Dhumbal, a culturally significant multiplayer card game with imperfect information, through a systematic comparison of rule-based, search-based, and learning-based strategies. We formalize Dhumbal's mechanics and implement diverse agents, including heuristic approaches (Aggressive, Conservative, Balanced, Opportunistic), search-based methods such as Monte Carlo Tree Search (MCTS) and Information Set Monte Carlo Tree Search (ISMCTS), and reinforcement learning approaches including Deep Q-Network (DQN) and Proximal Policy Optimization (PPO), and a random baseline. Evaluation involves within-category tournaments followed by a cross-category championship. Performance is measured via win rate, economic outcome, Jhyap success, cards discarded per round, risk assessment, and decision efficiency. Statistical significance is assessed using Welch's t-test with Bonferroni correction, effect sizes via Cohen's d, and 95% confidence intervals (CI). Across 1024 simulated rounds, the rule-based Aggressive agent achieves the highest win rate (88.3%, 95% CI: [86.3, 90.3]), outperforming ISMCTS (9.0%) and PPO (1.5%) through effective exploitation of Jhyap declarations. The study contributes a reproducible AI framework, insights into heuristic efficacy under partial information, and open-source code, thereby advancing AI research and supporting digital preservation of cultural games.

On April 13th, 2019, OpenAI Five became the first AI system to defeat the world champions at an esports game. The game of Dota 2 presents novel challenges for AI systems such as long time horizons, imperfect information, and complex, continuous state-action spaces, all challenges which will become increasingly central to more capable AI systems. OpenAI Five leveraged existing reinforcement learning techniques, scaled to learn from batches of approximately 2 million frames every 2 seconds. We developed a distributed training system and tools for continual training which allowed us to train OpenAI Five for 10 months. By defeating the Dota 2 world champion (Team OG), OpenAI Five demonstrates that self-play reinforcement learning can achieve superhuman performance on a difficult task.

Competitive Pok\'emon Singles (CPS) is a popular strategy game where players learn to exploit their opponent based on imperfect information in battles that can last more than one hundred stochastic turns. AI research in CPS has been led by heuristic tree search and online self-play, but the game may also create a platform to study adaptive policies trained offline on large datasets. We develop a pipeline to reconstruct the first-person perspective of an agent from logs saved from the third-person perspective of a spectator, thereby unlocking a dataset of real human battles spanning more than a decade that grows larger every day. This dataset enables a black-box approach where we train large sequence models to adapt to their opponent based solely on their input trajectory while selecting moves without explicit search of any kind. We study a progression from imitation learning to offline RL and offline fine-tuning on self-play data in the hardcore competitive setting of Pok\'emon's four oldest (and most partially observed) game generations. The resulting agents outperform a recent LLM Agent approach and a strong heuristic search engine. While playing anonymously in online battles against humans, our best agents climb to rankings inside the top 10% of active players.