Daily Papers

Black-box distillation creates student large language models (LLMs) by learning from a proprietary teacher model's text outputs alone, without access to its internal logits or parameters. In this work, we introduce Generative Adversarial Distillation (GAD), which enables on-policy and black-box distillation. GAD frames the student LLM as a generator and trains a discriminator to distinguish its responses from the teacher LLM's, creating a minimax game. The discriminator acts as an on-policy reward model that co-evolves with the student, providing stable, adaptive feedback. Experimental results show that GAD consistently surpasses the commonly used sequence-level knowledge distillation. In particular, Qwen2.5-14B-Instruct (student) trained with GAD becomes comparable to its teacher, GPT-5-Chat, on the LMSYS-Chat automatic evaluation. The results establish GAD as a promising and effective paradigm for black-box LLM distillation.

Conventional zero-shot learning (ZSL) methods generally learn an embedding, e.g., visual-semantic mapping, to handle the unseen visual samples via an indirect manner. In this paper, we take the advantage of generative adversarial networks (GANs) and propose a novel method, named leveraging invariant side GAN (LisGAN), which can directly generate the unseen features from random noises which are conditioned by the semantic descriptions. Specifically, we train a conditional Wasserstein GANs in which the generator synthesizes fake unseen features from noises and the discriminator distinguishes the fake from real via a minimax game. Considering that one semantic description can correspond to various synthesized visual samples, and the semantic description, figuratively, is the soul of the generated features, we introduce soul samples as the invariant side of generative zero-shot learning in this paper. A soul sample is the meta-representation of one class. It visualizes the most semantically-meaningful aspects of each sample in the same category. We regularize that each generated sample (the varying side of generative ZSL) should be close to at least one soul sample (the invariant side) which has the same class label with it. At the zero-shot recognition stage, we propose to use two classifiers, which are deployed in a cascade way, to achieve a coarse-to-fine result. Experiments on five popular benchmarks verify that our proposed approach can outperform state-of-the-art methods with significant improvements.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

Recent advances in Competitive Self-Play (CSP) have achieved, or even surpassed, human level performance in complex game environments such as Dota 2 and StarCraft II using Distributed Multi-Agent Reinforcement Learning (MARL). One core component of these methods relies on creating a pool of learning agents -- consisting of the Main Agent, past versions of this agent, and Exploiter Agents -- where Exploiter Agents learn counter-strategies to the Main Agents. A key drawback of these approaches is the large computational cost and physical time that is required to train the system, making them impractical to deploy in highly iterative real-life settings such as video game productions. In this paper, we propose the Minimax Exploiter, a game theoretic approach to exploiting Main Agents that leverages knowledge of its opponents, leading to significant increases in data efficiency. We validate our approach in a diversity of settings, including simple turn based games, the arcade learning environment, and For Honor, a modern video game. The Minimax Exploiter consistently outperforms strong baselines, demonstrating improved stability and data efficiency, leading to a robust CSP-MARL method that is both flexible and easy to deploy.

We introduce Pok\'eChamp, a minimax agent powered by Large Language Models (LLMs) for Pok\'emon battles. Built on a general framework for two-player competitive games, Pok\'eChamp leverages the generalist capabilities of LLMs to enhance minimax tree search. Specifically, LLMs replace three key modules: (1) player action sampling, (2) opponent modeling, and (3) value function estimation, enabling the agent to effectively utilize gameplay history and human knowledge to reduce the search space and address partial observability. Notably, our framework requires no additional LLM training. We evaluate Pok\'eChamp in the popular Gen 9 OU format. When powered by GPT-4o, it achieves a win rate of 76% against the best existing LLM-based bot and 84% against the strongest rule-based bot, demonstrating its superior performance. Even with an open-source 8-billion-parameter Llama 3.1 model, Pok\'eChamp consistently outperforms the previous best LLM-based bot, Pok\'ellmon powered by GPT-4o, with a 64% win rate. Pok\'eChamp attains a projected Elo of 1300-1500 on the Pok\'emon Showdown online ladder, placing it among the top 30%-10% of human players. In addition, this work compiles the largest real-player Pok\'emon battle dataset, featuring over 3 million games, including more than 500k high-Elo matches. Based on this dataset, we establish a series of battle benchmarks and puzzles to evaluate specific battling skills. We further provide key updates to the local game engine. We hope this work fosters further research that leverage Pok\'emon battle as benchmark to integrate LLM technologies with game-theoretic algorithms addressing general multiagent problems. Videos, code, and dataset available at https://sites.google.com/view/pokechamp-llm.

In this paper, we extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We propose mean-field Langevin averaged gradient (MFL-AG), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed Nash equilibrium. We also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. Furthermore, we propose mean-field Langevin anchored best response (MFL-ABR), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. Finally, we study applications to zero-sum Markov games and conduct simulations demonstrating long-term optimality.

This paper presents novel game-playing AI agents based on the AlphaZero framework, enhanced with Vision Transformer (ViT): AlphaViT, AlphaViD, and AlphaVDA. These agents are designed to play multiple board games of various sizes using a single network with shared weights, thereby overcoming AlphaZero's limitation of fixed-board-size constraints. AlphaViT employs only a transformer encoder, whereas AlphaViD and AlphaVDA incorporate both transformer encoders and decoders. In AlphaViD, the decoder processes outputs from the encoder, whereas AlphaVDA uses a learnable embeddings as the decoder input. The additional decoder layers in AlphaViD and AlphaVDA provide flexibility to adapt to various action spaces and board sizes. Experimental results show that the proposed agents, trained on either individual games or multiple games simultaneously, consistently outperform traditional algorithms such as Minimax and Monte Carlo Tree Search and approach the performance of AlphaZero, despite using a single deep neural network (DNN) with shared weights. In particular, AlphaViT shows strong performance across all tested games. Furthermore, fine-tuning the DNN using pre-trained weights from small-board games accelerates convergence and improves performance, particularly in Gomoku. Interestingly, simultaneous training on multiple games yields performance comparable to, or even surpassing, single-game training. These results indicate the potential of transformer-based architectures to develop more flexible and robust game-playing AI agents that excel in multiple games and dynamic environments.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood. In this work, we make the first attempt to theoretically understand the deep Q-network (DQN) algorithm (Mnih et al., 2015) from both algorithmic and statistical perspectives. In specific, we focus on a slight simplification of DQN that fully captures its key features. Under mild assumptions, we establish the algorithmic and statistical rates of convergence for the action-value functions of the iterative policy sequence obtained by DQN. In particular, the statistical error characterizes the bias and variance that arise from approximating the action-value function using deep neural network, while the algorithmic error converges to zero at a geometric rate. As a byproduct, our analysis provides justifications for the techniques of experience replay and target network, which are crucial to the empirical success of DQN. Furthermore, as a simple extension of DQN, we propose the Minimax-DQN algorithm for zero-sum Markov game with two players. Borrowing the analysis of DQN, we also quantify the difference between the policies obtained by Minimax-DQN and the Nash equilibrium of the Markov game in terms of both the algorithmic and statistical rates of convergence.

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel SelfishMPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses of all the neighbors of the action. This problem was introduced by mannor2011 and received considerable attention in recent years. It is generally stated in the literature that the minimax regret rate for this problem is of order alpha T, where alpha is the independence number of the graph, and T is the time horizon. However, this is proven only when the number of rounds T is larger than alpha^3, which poses a significant restriction for the usability of this result in large graphs. In this paper, we define a new quantity R^*, called the problem complexity, and prove that the minimax regret is proportional to R^* for any graph and time horizon T. Introducing an intricate exploration strategy, we define the \mainAlgorithm algorithm that achieves the minimax optimal regret bound and becomes the first provably optimal algorithm for this setting, even if T is smaller than alpha^3.

This paper introduces SC2LE (StarCraft II Learning Environment), a reinforcement learning environment based on the StarCraft II game. This domain poses a new grand challenge for reinforcement learning, representing a more difficult class of problems than considered in most prior work. It is a multi-agent problem with multiple players interacting; there is imperfect information due to a partially observed map; it has a large action space involving the selection and control of hundreds of units; it has a large state space that must be observed solely from raw input feature planes; and it has delayed credit assignment requiring long-term strategies over thousands of steps. We describe the observation, action, and reward specification for the StarCraft II domain and provide an open source Python-based interface for communicating with the game engine. In addition to the main game maps, we provide a suite of mini-games focusing on different elements of StarCraft II gameplay. For the main game maps, we also provide an accompanying dataset of game replay data from human expert players. We give initial baseline results for neural networks trained from this data to predict game outcomes and player actions. Finally, we present initial baseline results for canonical deep reinforcement learning agents applied to the StarCraft II domain. On the mini-games, these agents learn to achieve a level of play that is comparable to a novice player. However, when trained on the main game, these agents are unable to make significant progress. Thus, SC2LE offers a new and challenging environment for exploring deep reinforcement learning algorithms and architectures.

In this paper, we study the role of feedback in online learning with switching costs. It has been shown that the minimax regret is Theta(T^{2/3}) under bandit feedback and improves to Theta(T) under full-information feedback, where T is the length of the time horizon. However, it remains largely unknown how the amount and type of feedback generally impact regret. To this end, we first consider the setting of bandit learning with extra observations; that is, in addition to the typical bandit feedback, the learner can freely make a total of B_{ex} extra observations. We fully characterize the minimax regret in this setting, which exhibits an interesting phase-transition phenomenon: when B_{ex} = O(T^{2/3}), the regret remains Theta(T^{2/3}), but when B_{ex} = Omega(T^{2/3}), it becomes Theta(T/B_{mathrm{ex}}), which improves as the budget B_{ex} increases. To design algorithms that can achieve the minimax regret, it is instructive to consider a more general setting where the learner has a budget of B total observations. We fully characterize the minimax regret in this setting as well and show that it is Theta(T/B), which scales smoothly with the total budget B. Furthermore, we propose a generic algorithmic framework, which enables us to design different learning algorithms that can achieve matching upper bounds for both settings based on the amount and type of feedback. One interesting finding is that while bandit feedback can still guarantee optimal regret when the budget is relatively limited, it no longer suffices to achieve optimal regret when the budget is relatively large.

We introduce MiniMax-M1, the world's first open-weight, large-scale hybrid-attention reasoning model. MiniMax-M1 is powered by a hybrid Mixture-of-Experts (MoE) architecture combined with a lightning attention mechanism. The model is developed based on our previous MiniMax-Text-01 model, which contains a total of 456 billion parameters with 45.9 billion parameters activated per token. The M1 model natively supports a context length of 1 million tokens, 8x the context size of DeepSeek R1. Furthermore, the lightning attention mechanism in MiniMax-M1 enables efficient scaling of test-time compute. These properties make M1 particularly suitable for complex tasks that require processing long inputs and thinking extensively. MiniMax-M1 is trained using large-scale reinforcement learning (RL) on diverse problems including sandbox-based, real-world software engineering environments. In addition to M1's inherent efficiency advantage for RL training, we propose CISPO, a novel RL algorithm to further enhance RL efficiency. CISPO clips importance sampling weights rather than token updates, outperforming other competitive RL variants. Combining hybrid-attention and CISPO enables MiniMax-M1's full RL training on 512 H800 GPUs to complete in only three weeks, with a rental cost of just $534,700. We release two versions of MiniMax-M1 models with 40K and 80K thinking budgets respectively, where the 40K model represents an intermediate phase of the 80K training. Experiments on standard benchmarks show that our models are comparable or superior to strong open-weight models such as the original DeepSeek-R1 and Qwen3-235B, with particular strengths in complex software engineering, tool utilization, and long-context tasks. We publicly release MiniMax-M1 at https://github.com/MiniMax-AI/MiniMax-M1.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

The rapid advancement of large language models (LLMs) has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate LLMs' strategic reasoning capabilities, game theory, with its concise structure, has become a preferred approach. However, current research focuses on a limited selection of games, resulting in low coverage. Classic game scenarios risk data leakage, and existing benchmarks often lack extensibility, making them inadequate for evaluating state-of-the-art models. To address these challenges, we propose TMGBench, a benchmark with comprehensive game type coverage, novel scenarios, and flexible organization. Specifically, we incorporate all 144 game types summarized by the Robinson-Goforth topology of 2x2 games, constructed as classic games. We also employ synthetic data generation to create diverse, higher-quality scenarios through topic guidance and human inspection, referred to as story-based games. Lastly, we provide a sustainable framework for increasingly powerful LLMs by treating these games as atomic units and organizing them into more complex forms via sequential, parallel, and nested structures. Our comprehensive evaluation of mainstream LLMs covers tests on rational reasoning, robustness, Theory-of-Mind (ToM), and reasoning in complex forms. Results reveal flaws in accuracy, consistency, and varying mastery of ToM. Additionally, o1-mini, OpenAI's latest reasoning model, achieved accuracy rates of 66.6%, 60.0%, and 70.0% on sequential, parallel, and nested games, highlighting TMGBench's challenges.

In light of the burgeoning success of reinforcement learning (RL) in diverse real-world applications, considerable focus has been directed towards ensuring RL policies are robust to adversarial attacks during test time. Current approaches largely revolve around solving a minimax problem to prepare for potential worst-case scenarios. While effective against strong attacks, these methods often compromise performance in the absence of attacks or the presence of only weak attacks. To address this, we study policy robustness under the well-accepted state-adversarial attack model, extending our focus beyond only worst-case attacks. We first formalize this task at test time as a regret minimization problem and establish its intrinsic hardness in achieving sublinear regret when the baseline policy is from a general continuous policy class, Pi. This finding prompts us to refine the baseline policy class Pi prior to test time, aiming for efficient adaptation within a finite policy class Pi, which can resort to an adversarial bandit subroutine. In light of the importance of a small, finite Pi, we propose a novel training-time algorithm to iteratively discover non-dominated policies, forming a near-optimal and minimal Pi, thereby ensuring both robustness and test-time efficiency. Empirical validation on the Mujoco corroborates the superiority of our approach in terms of natural and robust performance, as well as adaptability to various attack scenarios.

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve Oleft(Delta^{1/4}T^{3/4}right) regret when the degree of nonstationarity, as measured by total variation Delta, is known, and Oleft(Delta^{1/5}T^{4/5}right) regret when Delta is unknown, where T is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

We study the problem of online learning in a two-player decentralized cooperative Stackelberg game. In each round, the leader first takes an action, followed by the follower who takes their action after observing the leader's move. The goal of the leader is to learn to minimize the cumulative regret based on the history of interactions. Differing from the traditional formulation of repeated Stackelberg games, we assume the follower is omniscient, with full knowledge of the true reward, and that they always best-respond to the leader's actions. We analyze the sample complexity of regret minimization in this repeated Stackelberg game. We show that depending on the reward structure, the existence of the omniscient follower may change the sample complexity drastically, from constant to exponential, even for linear cooperative Stackelberg games. This poses unique challenges for the learning process of the leader and the subsequent regret analysis.

Multi-agent reinforcement learning (MARL) has been shown effective for cooperative games in recent years. However, existing state-of-the-art methods face challenges related to sample complexity, training instability, and the risk of converging to a suboptimal Nash Equilibrium. In this paper, we propose a unified framework for learning stochastic policies to resolve these issues. We embed cooperative MARL problems into probabilistic graphical models, from which we derive the maximum entropy (MaxEnt) objective for MARL. Based on the MaxEnt framework, we propose Heterogeneous-Agent Soft Actor-Critic (HASAC) algorithm. Theoretically, we prove the monotonic improvement and convergence to quantal response equilibrium (QRE) properties of HASAC. Furthermore, we generalize a unified template for MaxEnt algorithmic design named Maximum Entropy Heterogeneous-Agent Mirror Learning (MEHAML), which provides any induced method with the same guarantees as HASAC. We evaluate HASAC on six benchmarks: Bi-DexHands, Multi-Agent MuJoCo, StarCraft Multi-Agent Challenge, Google Research Football, Multi-Agent Particle Environment, and Light Aircraft Game. Results show that HASAC consistently outperforms strong baselines, exhibiting better sample efficiency, robustness, and sufficient exploration.

In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a network that estimates joint action-values as a complex non-linear combination of per-agent values that condition only on local observations. We structurally enforce that the joint-action value is monotonic in the per-agent values, which allows tractable maximisation of the joint action-value in off-policy learning, and guarantees consistency between the centralised and decentralised policies. We evaluate QMIX on a challenging set of StarCraft II micromanagement tasks, and show that QMIX significantly outperforms existing value-based multi-agent reinforcement learning methods.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@k: the agent may submit up to k responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@k inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with k and the sampling budget N. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the N samples before selecting the top-k rewards. We prove that when the sampling budget is N=tildeOmega(C^*), the regret of BoM is O(epsilon_{opt}+epsilon_{mathrm{RM}^2C^*/k}), where C^* is the coverage coefficient, epsilon_{RM} is the estimation error of the reward model, and epsilon_{opt} is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing N. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Game theory, as an analytical tool, is frequently utilized to analyze human behavior in social science research. With the high alignment between the behavior of Large Language Models (LLMs) and humans, a promising research direction is to employ LLMs as substitutes for humans in game experiments, enabling social science research. However, despite numerous empirical researches on the combination of LLMs and game theory, the capability boundaries of LLMs in game theory remain unclear. In this research, we endeavor to systematically analyze LLMs in the context of game theory. Specifically, rationality, as the fundamental principle of game theory, serves as the metric for evaluating players' behavior -- building a clear desire, refining belief about uncertainty, and taking optimal actions. Accordingly, we select three classical games (dictator game, Rock-Paper-Scissors, and ring-network game) to analyze to what extent LLMs can achieve rationality in these three aspects. The experimental results indicate that even the current state-of-the-art LLM (GPT-4) exhibits substantial disparities compared to humans in game theory. For instance, LLMs struggle to build desires based on uncommon preferences, fail to refine belief from many simple patterns, and may overlook or modify refined belief when taking actions. Therefore, we consider that introducing LLMs into game experiments in the field of social science should be approached with greater caution.

Minimax problems are notoriously challenging to optimize. However, we demonstrate that the two-timescale extragradient can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under a mild condition. This work surpasses all previous results as we eliminate a crucial assumption that the Hessian, with respect to the maximization variable, is nondegenerate.

We present Mini-BEHAVIOR, a novel benchmark for embodied AI that challenges agents to use reasoning and decision-making skills to solve complex activities that resemble everyday human challenges. The Mini-BEHAVIOR environment is a fast, realistic Gridworld environment that offers the benefits of rapid prototyping and ease of use while preserving a symbolic level of physical realism and complexity found in complex embodied AI benchmarks. We introduce key features such as procedural generation, to enable the creation of countless task variations and support open-ended learning. Mini-BEHAVIOR provides implementations of various household tasks from the original BEHAVIOR benchmark, along with starter code for data collection and reinforcement learning agent training. In essence, Mini-BEHAVIOR offers a fast, open-ended benchmark for evaluating decision-making and planning solutions in embodied AI. It serves as a user-friendly entry point for research and facilitates the evaluation and development of solutions, simplifying their assessment and development while advancing the field of embodied AI. Code is publicly available at https://github.com/StanfordVL/mini_behavior.

There has been a recent surge of interest in developing generally-capable agents that can adapt to new tasks without additional training in the environment. Learning world models from reward-free exploration is a promising approach, and enables policies to be trained using imagined experience for new tasks. However, achieving a general agent requires robustness across different environments. In this work, we address the novel problem of generating curricula in the reward-free setting to train robust world models. We consider robustness in terms of minimax regret over all environment instantiations and show that the minimax regret can be connected to minimising the maximum error in the world model across environment instances. This result informs our algorithm, WAKER: Weighted Acquisition of Knowledge across Environments for Robustness. WAKER selects environments for data collection based on the estimated error of the world model for each environment. Our experiments demonstrate that WAKER outperforms several baselines, resulting in improved robustness, efficiency, and generalisation.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Effective macroeconomic policies play a crucial role in promoting economic growth and social stability. This paper models the optimal macroeconomic policy problem based on the Stackelberg Mean Field Game (SMFG), where the government acts as the leader in policy-making, and large-scale households dynamically respond as followers. This modeling method captures the asymmetric dynamic game between the government and large-scale households, and interpretably evaluates the effects of macroeconomic policies based on microfoundations, which is difficult for existing methods to achieve. We also propose a solution for SMFGs, incorporating pre-training on real data and a model-free Stackelberg mean-field reinforcement learning (SMFRL) algorithm, which operates independently of prior environmental knowledge and transitions. Our experimental results showcase the superiority of the SMFG method over other economic policies in terms of performance, efficiency-equity tradeoff, and SMFG assumption analysis. This paper significantly contributes to the domain of AI for economics by providing a powerful tool for modeling and solving optimal macroeconomic policies.

We study the Levine hat problem, a classic combinatorial puzzle introduced by Lionel Levine in 2010. This problem involves a game in which n geq 2 players, each seeing an infinite stack of hats on each of their teammates' heads but not on their own, must simultaneously guess the index of a black hat on their own stack. If one of the players fails to do so, the team loses collectively. The players must therefore come up with a good strategy before the game starts. While the optimal winning probability V_{n} remains unknown even for n=2, we make three key advances. First, we develop a novel geometric framework for representing strategies through measurable functions, providing a new expression of V_{n} and a unified treatment of the game for finite and for infinite stacks via integral formulations. Secondly, we construct a new strategy K_{5} that reaches the conjectured optimal probability of victory : 0.35. We also show that K_{5} is part of a larger class of strategies that allow us to improve current bounds and resolve conjectured inequalities. Finally, we introduce and entirely solve a continuous generalization of the problem, demonstrating that extending to uncountable hat stacks increases the optimal winning probability to exactly 1/2. This generalization naturally leads to a broader and smoother strategic framework, within which we also describe how to compute optimal responses to a range of strategies.

When reward functions are hand-designed, deep reinforcement learning algorithms often suffer from reward misspecification, causing them to learn suboptimal policies in terms of the intended task objectives. In the single-agent case, inverse reinforcement learning (IRL) techniques attempt to address this issue by inferring the reward function from expert demonstrations. However, in multi-agent problems, misalignment between the learned and true objectives is exacerbated due to increased environment non-stationarity and variance that scales with multiple agents. As such, in multi-agent general-sum games, multi-agent IRL algorithms have difficulty balancing cooperative and competitive objectives. To address these issues, we propose Multi-Agent Marginal Q-Learning from Demonstrations (MAMQL), a novel sample-efficient framework for multi-agent IRL. For each agent, MAMQL learns a critic marginalized over the other agents' policies, allowing for a well-motivated use of Boltzmann policies in the multi-agent context. We identify a connection between optimal marginalized critics and single-agent soft-Q IRL, allowing us to apply a direct, simple optimization criterion from the single-agent domain. Across our experiments on three different simulated domains, MAMQL significantly outperforms previous multi-agent methods in average reward, sample efficiency, and reward recovery by often more than 2-5x. We make our code available at https://sites.google.com/view/mamql .

The game show Lucky 13 differs from other television game shows in that contestants are required to place a bet on their own knowledge of trivia by selecting a range that contains the number of questions that they answered correctly. We present a model for this game show using binomial random variables and generate tables outlining the optimal range the player should select based on maximization of two different utility functions. After analyzing the decisions made by some actual contestants on this show, we present a numerical simulation for how many questions an average player is expected to answer correctly based on question categories observed for two sample contestants.

In multi-agent reinforcement learning (MARL), independent learning (IL) often shows remarkable performance and easily scales with the number of agents. Yet, using IL can be inefficient and runs the risk of failing to successfully train, particularly in scenarios that require agents to coordinate their actions. Using centralised learning (CL) enables MARL agents to quickly learn how to coordinate their behaviour but employing CL everywhere is often prohibitively expensive in real-world applications. Besides, using CL in value-based methods often needs strong representational constraints (e.g. individual-global-max condition) that can lead to poor performance if violated. In this paper, we introduce a novel plug & play IL framework named Multi-Agent Network Selection Algorithm (MANSA) which selectively employs CL only at states that require coordination. At its core, MANSA has an additional agent that uses switching controls to quickly learn the best states to activate CL during training, using CL only where necessary and vastly reducing the computational burden of CL. Our theory proves MANSA preserves cooperative MARL convergence properties, boosts IL performance and can optimally make use of a fixed budget on the number CL calls. We show empirically in Level-based Foraging (LBF) and StarCraft Multi-agent Challenge (SMAC) that MANSA achieves fast, superior and more reliable performance while making 40% fewer CL calls in SMAC and using CL at only 1% CL calls in LBF.

Classical convergence guarantees for gradient-based learning in games require the pseudo-gradient to be (strongly) monotone in Euclidean geometry as shown by rosen(1965), a condition that often fails even in simple games with strong cross-player couplings. We introduce Small-Gain Nash (SGN), a block small-gain condition in a custom block-weighted geometry. SGN converts local curvature and cross-player Lipschitz coupling bounds into a tractable certificate of contraction. It constructs a weighted block metric in which the pseudo-gradient becomes strongly monotone on any region where these bounds hold, even when it is non-monotone in the Euclidean sense. The continuous flow is exponentially contracting in this designed geometry, and projected Euler and RK4 discretizations converge under explicit step-size bounds derived from the SGN margin and a local Lipschitz constant. Our analysis reveals a certified ``timescale band'', a non-asymptotic, metric-based certificate that plays a TTUR-like role: rather than forcing asymptotic timescale separation via vanishing, unequal step sizes, SGN identifies a finite band of relative metric weights for which a single-step-size dynamics is provably contractive. We validate the framework on quadratic games where Euclidean monotonicity analysis fails to predict convergence, but SGN successfully certifies it, and extend the construction to mirror/Fisher geometries for entropy-regularized policy gradient in Markov games. The result is an offline certification pipeline that estimates curvature, coupling, and Lipschitz parameters on compact regions, optimizes block weights to enlarge the SGN margin, and returns a structural, computable convergence certificate consisting of a metric, contraction rate, and safe step-sizes for non-monotone games.

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

Card games are widely used to study sequential decision-making under uncertainty, with real-world analogues in negotiation, finance, and cybersecurity. These games typically fall into three categories based on the flow of control: strictly sequential (players alternate single actions), deterministic response (some actions trigger a fixed outcome), and unbounded reciprocal response (alternating counterplays are permitted). A less-explored but strategically rich structure is the bounded one-sided response, where a player's action briefly transfers control to the opponent, who must satisfy a fixed condition through one or more moves before the turn resolves. We term games featuring this mechanism Bounded One-Sided Response Games (BORGs). We introduce a modified version of Monopoly Deal as a benchmark environment that isolates this dynamic, where a Rent action forces the opponent to choose payment assets. The gold-standard algorithm, Counterfactual Regret Minimization (CFR), converges on effective strategies without novel algorithmic extensions. A lightweight full-stack research platform unifies the environment, a parallelized CFR runtime, and a human-playable web interface. The trained CFR agent and source code are available at https://monopolydeal.ai.

Multi-agent football poses an unsolved challenge in AI research. Existing work has focused on tackling simplified scenarios of the game, or else leveraging expert demonstrations. In this paper, we develop a multi-agent system to play the full 11 vs. 11 game mode, without demonstrations. This game mode contains aspects that present major challenges to modern reinforcement learning algorithms; multi-agent coordination, long-term planning, and non-transitivity. To address these challenges, we present TiZero; a self-evolving, multi-agent system that learns from scratch. TiZero introduces several innovations, including adaptive curriculum learning, a novel self-play strategy, and an objective that optimizes the policies of multiple agents jointly. Experimentally, it outperforms previous systems by a large margin on the Google Research Football environment, increasing win rates by over 30%. To demonstrate the generality of TiZero's innovations, they are assessed on several environments beyond football; Overcooked, Multi-agent Particle-Environment, Tic-Tac-Toe and Connect-Four.

We study an online learning problem in general-sum Stackelberg games, where players act in a decentralized and strategic manner. We study two settings depending on the type of information for the follower: (1) the limited information setting where the follower only observes its own reward, and (2) the side information setting where the follower has extra side information about the leader's reward. We show that for the follower, myopically best responding to the leader's action is the best strategy for the limited information setting, but not necessarily so for the side information setting -- the follower can manipulate the leader's reward signals with strategic actions, and hence induce the leader's strategy to converge to an equilibrium that is better off for itself. Based on these insights, we study decentralized online learning for both players in the two settings. Our main contribution is to derive last-iterate convergence and sample complexity results in both settings. Notably, we design a new manipulation strategy for the follower in the latter setting, and show that it has an intrinsic advantage against the best response strategy. Our theories are also supported by empirical results.

The utilization of artificial intelligence (AI) in card games has been a well-explored subject within AI research for an extensive period. Recent advancements have propelled AI programs to showcase expertise in intricate card games such as Mahjong, DouDizhu, and Texas Hold'em. In this work, we aim to develop an AI program for an exceptionally complex and popular card game called GuanDan. This game involves four players engaging in both competitive and cooperative play throughout a long process to upgrade their level, posing great challenges for AI due to its expansive state and action space, long episode length, and complex rules. Employing reinforcement learning techniques, specifically Deep Monte Carlo (DMC), and a distributed training framework, we first put forward an AI program named DanZero for this game. Evaluation against baseline AI programs based on heuristic rules highlights the outstanding performance of our bot. Besides, in order to further enhance the AI's capabilities, we apply policy-based reinforcement learning algorithm to GuanDan. To address the challenges arising from the huge action space, which will significantly impact the performance of policy-based algorithms, we adopt the pre-trained model to facilitate the training process and the achieved AI program manages to achieve a superior performance.

We introduce Atla Selene Mini, a state-of-the-art small language model-as-a-judge (SLMJ). Selene Mini is a general-purpose evaluator that outperforms the best SLMJs and GPT-4o-mini on overall performance across 11 out-of-distribution benchmarks, spanning absolute scoring, classification, and pairwise preference tasks. It is the highest-scoring 8B generative model on RewardBench, surpassing strong baselines like GPT-4o and specialized judges. To achieve this, we develop a principled data curation strategy that augments public datasets with synthetically generated critiques and ensures high quality through filtering and dataset ablations. We train our model on a combined direct preference optimization (DPO) and supervised fine-tuning (SFT) loss, and produce a highly promptable evaluator that excels in real-world scenarios. Selene Mini shows dramatically improved zero-shot agreement with human expert evaluations on financial and medical industry datasets. It is also robust to variations in prompt format. Preliminary results indicate that Selene Mini is the top-ranking evaluator in a live, community-driven Judge Arena. We release the model weights on HuggingFace (https://hf.co/AtlaAI/Selene-1-Mini-Llama-3.1-8B) and Ollama to encourage widespread community adoption.

Assistance games are a promising alternative to reinforcement learning from human feedback (RLHF) for training AI assistants. Assistance games resolve key drawbacks of RLHF, such as incentives for deceptive behavior, by explicitly modeling the interaction between assistant and user as a two-player game where the assistant cannot observe their shared goal. Despite their potential, assistance games have only been explored in simple settings. Scaling them to more complex environments is difficult because it requires both solving intractable decision-making problems under uncertainty and accurately modeling human users' behavior. We present the first scalable approach to solving assistance games and apply it to a new, challenging Minecraft-based assistance game with over 10^{400} possible goals. Our approach, AssistanceZero, extends AlphaZero with a neural network that predicts human actions and rewards, enabling it to plan under uncertainty. We show that AssistanceZero outperforms model-free RL algorithms and imitation learning in the Minecraft-based assistance game. In a human study, our AssistanceZero-trained assistant significantly reduces the number of actions participants take to complete building tasks in Minecraft. Our results suggest that assistance games are a tractable framework for training effective AI assistants in complex environments. Our code and models are available at https://github.com/cassidylaidlaw/minecraft-building-assistance-game.

Playing games has a long history of describing intricate interactions in simplified forms. In this paper we explore if large language models (LLMs) can play games, investigating their capabilities for randomisation and strategic adaptation through both simultaneous and sequential game interactions. We focus on GPT-4o-Mini-2024-08-17 and test two games between LLMs: Rock Paper Scissors (RPS) and games of strategy (Prisoners Dilemma PD). LLMs are often described as stochastic parrots, and while they may indeed be parrots, our results suggest that they are not very stochastic in the sense that their outputs - when prompted to be random - are often very biased. Our research reveals that LLMs appear to develop loss aversion strategies in repeated games, with RPS converging to stalemate conditions while PD shows systematic shifts between cooperative and competitive outcomes based on prompt design. We detail programmatic tools for independent agent interactions and the Agentic AI challenges faced in implementation. We show that LLMs can indeed play games, just not very well. These results have implications for the use of LLMs in multi-agent LLM systems and showcase limitations in current approaches to model output for strategic decision-making.

Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order {Omega}Bigl( H^3SA{epsilon^2} bigl( log bigl(1{delta}bigl) + S bigl)Bigl), being S and A the number of states and actions respectively, H the horizon, epsilon the desired accuracy, and delta the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.

Motivated by the phenomenon of strategic agents gaming a recommender system to maximize the number of times they are recommended to users, we study a strategic variant of the linear contextual bandit problem, where the arms can strategically misreport privately observed contexts to the learner. We treat the algorithm design problem as one of mechanism design under uncertainty and propose the Optimistic Grim Trigger Mechanism (OptGTM) that incentivizes the agents (i.e., arms) to report their contexts truthfully while simultaneously minimizing regret. We also show that failing to account for the strategic nature of the agents results in linear regret. However, a trade-off between mechanism design and regret minimization appears to be unavoidable. More broadly, this work aims to provide insight into the intersection of online learning and mechanism design.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules.

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.

Game-playing agents like AlphaGo have achieved superhuman performance through self-play, which is theoretically guaranteed to yield optimal policies in competitive games. However, most language tasks are partially or fully cooperative, so it is an open question whether techniques like self-play can effectively be used to improve language models. We empirically investigate this question in a negotiation game setting known as Deal or No Deal (DoND). Crucially, the objective in DoND can be modified to produce a fully cooperative game, a strictly competitive one, or anything in between. We finetune language models in self-play over multiple rounds of filtered behavior cloning in DoND for each of these objectives. Contrary to expectations, we find that language model self-play leads to significant performance gains in both cooperation and competition with humans, suggesting that self-play and related techniques have promise despite a lack of theoretical guarantees.