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Stephen Marcus McAleer

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19 papers

2 author rows

AAAI Conference 2026 Conference Paper

Faster Game Solving via Hyperparameter Schedules

Naifeng Zhang
Stephen Marcus McAleer
Tuomas Sandholm

Counterfactual regret minimization (CFR) algorithms are a foundational class of methods for solving imperfect-information games, with the time average of their iterates converging to a Nash equilibrium in two-player zero-sum games. Prior state-of-the-art variants, Discounted CFR (DCFR) and Predictive CFR+ (PCFR+), achieved the fastest known practical performance by improving convergence rates over vanilla CFR through discounting early iterations with a fixed discounting scheme. More recently, Dynamic DCFR (DDCFR) introduced agent-learned dynamic discounting schemes to further accelerate convergence, at the cost of increased complexity. To address this, we propose Hyperparameter Schedules (HSs), a remarkably simple, training-free framework that dynamically adjusts CFR discounting over time. HSs aggressively downweight early updates and gradually transition to trusting late-stage strategies, leading to substantially faster convergence with only a few lines of code modifications. We show that HSs derived from just three small extensive-form games generalize effectively to 17 diverse games (including large-scale realistic poker) in both extensive-form and normal-form settings, without any game-specific tuning. Our method establishes a new state of the art for solving two-player zero-sum games.

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TMLR Journal 2025 Journal Article

Tree Search for Language Model Agents

Jing Yu Koh
Stephen Marcus McAleer
Daniel Fried
Ruslan Salakhutdinov

Autonomous agents powered by language models (LMs) have demonstrated promise in their ability to perform decision-making tasks such as web automation. However, a key limitation remains: LMs, primarily optimized for natural language understanding and generation, struggle with multi-step reasoning, planning, and using environmental feedback when attempting to solve realistic computer tasks. Towards addressing this, we propose an inference-time search algorithm for LM agents to explicitly perform exploration and multi-step planning in interactive web environments. Our approach is a form of best-first tree search that operates within the actual environment space, and is complementary with most existing state-of-the-art agents. It is the first tree search algorithm for LM agents that shows effectiveness on realistic web tasks. On the challenging VisualWebArena benchmark, applying our search algorithm on top of a GPT-4o agent yields a 39.7% relative increase in success rate compared to the same baseline without search, setting a state-of-the-art success rate of 26.4%. On WebArena, search also yields a 28.0% relative improvement over a baseline agent, setting a competitive success rate of 19.2%. Our experiments showcase the effectiveness of search for web agents, and we demonstrate that performance scales with increased test-time compute.

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ICML Conference 2024 Conference Paper

AlphaZero-Like Tree-Search can Guide Large Language Model Decoding and Training

Ziyu Wan
Xidong Feng
Muning Wen
Stephen Marcus McAleer
Ying Wen 0001
Weinan Zhang 0001
Jun Wang 0012

Recent works like Tree-of-Thought (ToT) and Reasoning via Planning (RAP) aim to augment the multi-step reasoning capabilities of LLMs by using tree-search algorithms. These methods rely on prompting a pre-trained model to serve as a value function and focus on problems with low search depth. As a result, these methods cannot benefit from in-domain training and only rely on pretraining process — they will not work in domains where the pre-trained LLM does not have enough knowledge to serve as an effective value function or in domains that require long-horizon planning. To address these limitations, we present an AlphaZero-like tree-search learning framework for LLMs (termed TS-LLM), systematically illustrating how tree-search with a learned value function can guide LLM decoding. TS-LLM distinguishes itself in two key ways. (1) Leveraging a learned value function and AlphaZero-like algorithms, our approach can be generally adaptable to a wide range of tasks, language models of any size, and tasks of varying search depths. (2) Our approach can guide LLMs during both inference and training, iteratively improving the LLMs. Empirical results across reasoning, planning, alignment, and decision-making tasks show that TS-LLM outperforms existing approaches and can handle trees with a depth of 64.

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ICLR Conference 2024 Conference Paper

Confronting Reward Model Overoptimization with Constrained RLHF

Ted Moskovitz
Aaditya K. Singh
DJ Strouse
Tuomas Sandholm
Ruslan Salakhutdinov
Anca D. Dragan
Stephen Marcus McAleer

Large language models are typically aligned with human preferences by optimizing reward models (RMs) fitted to human feedback. However, human preferences are multi-faceted, and it is increasingly common to derive reward from a composition of simpler reward models which each capture a different aspect of language quality. This itself presents a challenge, as it is difficult to appropriately weight these component RMs when combining them. Compounding this difficulty, because any RM is only a proxy for human evaluation, this process is vulnerable to *overoptimization*, wherein past a certain point, accumulating higher reward is associated with worse human ratings. In this paper, we perform the first study on overoptimization in composite RMs, showing that correlation between component RMs has a significant effect on the locations of these points. We then introduce an approach to solve this issue using constrained reinforcement learning as a means of preventing the agent from exceeding each RM's threshold of usefulness. Our method addresses the problem of weighting component RMs by learning dynamic weights, naturally given by the Lagrange multipliers. As a result, each RM stays within the range at which it is an effective proxy, improving evaluation performance. Finally, we introduce an adaptive method using gradient-free optimization to identify and optimize towards these points during a single run.

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ICLR Conference 2024 Conference Paper

Game-Theoretic Robust Reinforcement Learning Handles Temporally-Coupled Perturbations

Yongyuan Liang
Yanchao Sun
Ruijie Zheng
Xiangyu Liu
Benjamin Eysenbach
Tuomas Sandholm
Furong Huang
Stephen Marcus McAleer

Deploying reinforcement learning (RL) systems requires robustness to uncertainty and model misspecification, yet prior robust RL methods typically only study noise introduced independently across time. However, practical sources of uncertainty are usually coupled across time. We formally introduce temporally-coupled perturbations, presenting a novel challenge for existing robust RL methods. To tackle this challenge, we propose GRAD, a novel game-theoretic approach that treats the temporally-coupled robust RL problem as a partially-observable two-player zero-sum game. By finding an approximate equilibrium within this game, GRAD optimizes for general robustness against temporally-coupled perturbations. Experiments on continuous control tasks demonstrate that, compared with prior methods, our approach achieves a higher degree of robustness to various types of attacks on different attack domains, both in settings with temporally-coupled perturbations and decoupled perturbations.

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ICLR Conference 2024 Conference Paper

Illusory Attacks: Information-theoretic detectability matters in adversarial attacks

Tim Franzmeyer
Stephen Marcus McAleer
João F. Henriques
Jakob N. Foerster
Philip H. S. Torr
Adel Bibi
Christian Schröder de Witt

Autonomous agents deployed in the real world need to be robust against adversarial attacks on sensory inputs. Robustifying agent policies requires anticipating the strongest attacks possible. We demonstrate that existing observation-space attacks on reinforcement learning agents have a common weakness: while effective, their lack of information-theoretic detectability constraints makes them \textit{detectable} using automated means or human inspection. Detectability is undesirable to adversaries as it may trigger security escalations. We introduce \textit{\eattacks{}}, a novel form of adversarial attack on sequential decision-makers that is both effective and of $\epsilon-$bounded statistical detectability. We propose a novel dual ascent algorithm to learn such attacks end-to-end. Compared to existing attacks, we empirically find \eattacks{} to be significantly harder to detect with automated methods, and a small study with human participants\footnote{IRB approval under reference R84123/RE001} suggests they are similarly harder to detect for humans. Our findings suggest the need for better anomaly detectors, as well as effective hardware- and system-level defenses. The project website can be found at https://tinyurl.com/illusory-attacks.

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ICLR Conference 2024 Conference Paper

Llemma: An Open Language Model for Mathematics

Zhangir Azerbayev
Hailey Schoelkopf
Keiran Paster
Marco Dos Santos
Stephen Marcus McAleer
Albert Q. Jiang
Jia Deng
Stella Biderman

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known openly released models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

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PRL Workshop 2024 Workshop Paper

Q* Search: Heuristic Search with Deep Q-Networks

Forest Agostinelli
Shahaf S. Shperberg
Alexander Shmakov
Stephen Marcus McAleer
Roy Fox
Pierre Baldi

Efficiently solving problems with large action spaces using A* search has been of importance to the artificial intelligence community for decades. This is because the computation and memory requirements of A* search grow linearly with the size of the action space. This burden becomes even more apparent when A* search uses a heuristic function learned by computationally expensive function approximators, such as deep neural networks. To address this problem, we introduce Q* search, a search algorithm that uses deep Q-networks to guide search in order to take advantage of the fact that the sum of the transition costs and heuristic values of the children of a node can be computed with a single forward pass through a deep Q-network without explicitly generating those children. This significantly reduces computation time and requires only one node to be generated per iteration. We use Q* search on different domains and action spaces, showing that Q* suffers from only a small runtime overhead as the action size increases. In addition, our empirical results show Q* search is up to 129 times faster and generates up to 1288 times fewer nodes than A* search. Finally, although obtaining admissible heuristic functions from deep neural networks is an ongoing area of research, we prove that Q* search is guaranteed to find a shortest path given a heuristic function does not overestimate the sum of the transition cost and cost-to-go of the state.

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ICLR Conference 2024 Conference Paper

Toward Optimal Policy Population Growth in Two-Player Zero-Sum Games

Stephen Marcus McAleer
JB Lanier
Kevin A. Wang
Pierre Baldi
Tuomas Sandholm
Roy Fox

In competitive two-agent environments, deep reinforcement learning (RL) methods like Policy Space Response Oracles (PSRO) often increase exploitability between iterations, which is problematic when training in large games. To address this issue, we introduce anytime double oracle (ADO), an algorithm that ensures exploitability does not increase between iterations, and its approximate extensive-form version, anytime PSRO (APSRO). ADO converges to a Nash equilibrium while iteratively reducing exploitability. However, convergence in these algorithms may require adding all of a game's deterministic policies. To improve this, we propose Self-Play PSRO (SP-PSRO), which incorporates an approximately optimal stochastic policy into the population in each iteration. APSRO and SP-PSRO demonstrate lower exploitability and near-monotonic exploitability reduction in games like Leduc poker and Liar's Dice. Empirically, SP-PSRO often converges much faster than APSRO and PSRO, requiring only a few iterations in many games.

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ICML Conference 2023 Conference Paper

A Game-Theoretic Framework for Managing Risk in Multi-Agent Systems

Oliver Slumbers
David Henry Mguni
Stefano B. Blumberg
Stephen Marcus McAleer
Yaodong Yang 0001
Jun Wang 0012

In order for agents in multi-agent systems (MAS) to be safe, they need to take into account the risks posed by the actions of other agents. However, the dominant paradigm in game theory (GT) assumes that agents are not affected by risk from other agents and only strive to maximise their expected utility. For example, in hybrid human-AI driving systems, it is necessary to limit large deviations in reward resulting from car crashes. Although there are equilibrium concepts in game theory that take into account risk aversion, they either assume that agents are risk-neutral with respect to the uncertainty caused by the actions of other agents, or they are not guaranteed to exist. We introduce a new GT-based Risk-Averse Equilibrium (RAE) that always produces a solution that minimises the potential variance in reward accounting for the strategy of other agents. Theoretically and empirically, we show RAE shares many properties with a Nash Equilibrium (NE), establishing convergence properties and generalising to risk-dominant NE in certain cases. To tackle large-scale problems, we extend RAE to the PSRO multi-agent reinforcement learning (MARL) framework. We empirically demonstrate the minimum reward variance benefits of RAE in matrix games with high-risk outcomes. Results on MARL experiments show RAE generalises to risk-dominant NE in a trust dilemma game and that it reduces instances of crashing by 7x in an autonomous driving setting versus the best performing baseline.

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EWRL Workshop 2023 Workshop Paper

Automated Design of Affine Maximizer Mechanisms in Dynamic Settings

Michael Curry
Vinzenz Thoma
Darshan Chakrabarti
Stephen Marcus McAleer
Christian Kroer
Tuomas Sandholm
Niao He
Sven Seuken

Dynamic mechanism design is a challenging extension to ordinary mechanism design in which the mechanism designer must make a sequence of decisions over time in the face of possibly untruthful reports of participating agents. Optimizing dynamic mechanisms for welfare is relatively well understood. However, there has been less work on optimizing for other goals (e. g. revenue), and without restrictive assumptions on valuations, it is remarkably challenging to characterize good mechanisms. Instead, we turn to automated mechanism design to find mechanisms with good performance in specific problem instances. We extend the class of affine maximizer mechanisms to MDPs where agents may untruthfully report their rewards. This extension results in a challenging bilevel optimization problem in which the upper problem involves choosing optimal mechanism parameters, and the lower problem involves solving the resulting MDP. Our approach can find truthful dynamic mechanisms that achieve strong performance on goals other than welfare, and can be applied to essentially any problem setting---without restrictions on valuations---for which RL can learn optimal policies.

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ICLR Conference 2023 Conference Paper

ESCHER: Eschewing Importance Sampling in Games by Computing a History Value Function to Estimate Regret

Stephen Marcus McAleer
Gabriele Farina
Marc Lanctot
Tuomas Sandholm

Recent techniques for approximating Nash equilibria in very large games leverage neural networks to learn approximately optimal policies (strategies). One promis- ing line of research uses neural networks to approximate counterfactual regret minimization (CFR) or its modern variants. DREAM, the only current CFR-based neural method that is model free and therefore scalable to very large games, trains a neural network on an estimated regret target that can have extremely high variance due to an importance sampling term inherited from Monte Carlo CFR (MCCFR). In this paper we propose an unbiased model-free method that does not require any importance sampling. Our method, ESCHER, is principled and is guaranteed to converge to an approximate Nash equilibrium with high probability. We show that the variance of the estimated regret of ESCHER is orders of magnitude lower than DREAM and other baselines. We then show that ESCHER outperforms the prior state of the art—DREAM and neural fictitious self play (NFSP)—on a number of games and the difference becomes dramatic as game size increases. In the very large game of dark chess, ESCHER is able to beat DREAM and NFSP in a head-to-head competition over 90% of the time.

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TMLR Journal 2023 Journal Article

JiangJun: Mastering Xiangqi by Tackling Non-Transitivity in Two-Player Zero-Sum Games

Yang Li
Kun Xiong
Yingping Zhang
Jiangcheng Zhu
Stephen Marcus McAleer
Wei Pan
Jun Wang
Zonghong Dai

This paper presents an empirical exploration of non-transitivity in perfect-information games, specifically focusing on Xiangqi, a traditional Chinese board game comparable in game-tree complexity to chess and shogi. By analyzing over 10,000 records of human Xiangqi play, we highlight the existence of both transitive and non-transitive elements within the game’s strategic structure. To address non-transitivity, we introduce the JiangJun algorithm, an innovative combination of Monte-Carlo Tree Search (MCTS) and Policy Space Response Oracles (PSRO) designed to approximate a Nash equilibrium. We evaluate the algorithm empirically using a WeChat mini program and achieve a Master level with a 99.41% win rate against human players. The algorithm’s effectiveness in overcoming non-transitivity is confirmed by a plethora of metrics, such as relative population performance and visualization results. Our project site is available at https://sites.google.com/view/jiangjun-site/.

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ICML Conference 2023 Conference Paper

MANSA: Learning Fast and Slow in Multi-Agent Systems

David Henry Mguni
Haojun Chen
Taher Jafferjee
Jianhong Wang
Longfei Yue
Xidong Feng
Stephen Marcus McAleer
Feifei Tong

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.

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ICML Conference 2023 Conference Paper

Regret-Minimizing Double Oracle for Extensive-Form Games

Xiaohang Tang
Le Cong Dinh
Stephen Marcus McAleer
Yaodong Yang 0001

By incorporating regret minimization, double oracle methods have demonstrated rapid convergence to Nash Equilibrium (NE) in normal-form games and extensive-form games, through algorithms such as online double oracle (ODO) and extensive-form double oracle (XDO), respectively. In this study, we further examine the theoretical convergence rate and sample complexity of such regret minimization-based double oracle methods, utilizing a unified framework called Regret-Minimizing Double Oracle. Based on this framework, we extend ODO to extensive-form games and determine its sample complexity. Moreover, we demonstrate that the sample complexity of XDO can be exponential in the number of information sets $|S|$, owing to the exponentially decaying stopping threshold of restricted games. To solve this problem, we propose the Periodic Double Oracle (PDO) method, which has the lowest sample complexity among regret minimization-based double oracle methods, being only polynomial in $|S|$. Empirical evaluations on multiple poker and board games show that PDO achieves significantly faster convergence than previous double oracle algorithms and reaches a competitive level with state-of-the-art regret minimization methods.

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TMLR Journal 2022 Journal Article

Online Double Oracle

Le Cong Dinh
Stephen Marcus McAleer
Zheng Tian
Nicolas Perez-Nieves
Oliver Slumbers
David Henry Mguni
Jun Wang
Haitham Bou Ammar

Solving strategic games with huge action spaces is a critical yet under-explored topic in economics, operations research and artificial intelligence. This paper proposes new learning algorithms for solving two-player zero-sum normal-form games where the number of pure strategies is prohibitively large. Specifically, we combine no-regret analysis from online learning with Double Oracle (DO) from game theory. Our method---\emph{Online Double Oracle (ODO)}---is provably convergent to a Nash equilibrium (NE). Most importantly, unlike normal DO, ODO is \emph{rational} in the sense that each agent in ODO can exploit a strategic adversary with a regret bound of $\mathcal{O}(\sqrt{ k \log(k)/T})$, where $k$ is not the total number of pure strategies, but rather the size of \emph{effective strategy set}. In many applications, we empirically show that $k$ is linearly dependent on the support size of the NE. On tens of different real-world matrix games, ODO outperforms DO, PSRO, and no-regret algorithms such as Multiplicative Weights Update by a significant margin, both in terms of convergence rate to a NE, and average payoff against strategic adversaries.

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ICML Conference 2022 Conference Paper

Proving Theorems using Incremental Learning and Hindsight Experience Replay

Eser Aygün
Ankit Anand
Laurent Orseau
Xavier Glorot
Stephen Marcus McAleer
Vlad Firoiu
Lei M. Zhang
Doina Precup

Traditional automated theorem proving systems for first-order logic depend on speed-optimized search and many handcrafted heuristics designed to work over a wide range of domains. Machine learning approaches in the literature either depend on these traditional provers to bootstrap themselves, by leveraging these heuristics, or can struggle due to limited existing proof data. The latter issue can be explained by the lack of a smooth difficulty gradient in theorem proving datasets; large gaps in difficulty between different theorems can make training harder or even impossible. In this paper, we adapt the idea of hindsight experience replay from reinforcement learning to the automated theorem proving domain, so as to use the intermediate data generated during unsuccessful proof attempts. We build a first-order logic prover by disabling all the smart clause-scoring heuristics of the state-of-the-art E prover and replacing them with a clause-scoring neural network learned by using hindsight experience replay in an incremental learning setting. Clauses are represented as graphs and presented to transformer networks with spectral features. We show that provers trained in this way can outperform previous machine learning approaches and compete with the state of the art heuristic-based theorem prover E in its best configuration, on the popular benchmarks MPTP2078, M2k and Mizar40. The proofs generated by our algorithm are also almost always significantly shorter than E’s proofs.

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ICML Conference 2022 Conference Paper

Reducing Variance in Temporal-Difference Value Estimation via Ensemble of Deep Networks

Litian Liang
Yaosheng Xu
Stephen Marcus McAleer
Dailin Hu
Alexander Ihler
Pieter Abbeel
Roy Fox

In temporal-difference reinforcement learning algorithms, variance in value estimation can cause instability and overestimation of the maximal target value. Many algorithms have been proposed to reduce overestimation, including several recent ensemble methods, however none have shown success in sample-efficient learning through addressing estimation variance as the root cause of overestimation. In this paper, we propose MeanQ, a simple ensemble method that estimates target values as ensemble means. Despite its simplicity, MeanQ shows remarkable sample efficiency in experiments on the Atari Learning Environment benchmark. Importantly, we find that an ensemble of size 5 sufficiently reduces estimation variance to obviate the lagging target network, eliminating it as a source of bias and further gaining sample efficiency. We justify intuitively and empirically the design choices in MeanQ, including the necessity of independent experience sampling. On a set of 26 benchmark Atari environments, MeanQ outperforms all tested baselines, including the best available baseline, SUNRISE, at 100K interaction steps in 16/26 environments, and by 68% on average. MeanQ also outperforms Rainbow DQN at 500K steps in 21/26 environments, and by 49% on average, and achieves average human-level performance using 200K ($\pm$100K) interaction steps. Our implementation is available at https: //github. com/indylab/MeanQ.

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ICML Conference 2020 Conference Paper

Evolutionary Reinforcement Learning for Sample-Efficient Multiagent Coordination

Somdeb Majumdar
Shauharda Khadka
Santiago Miret
Stephen Marcus McAleer
Kagan Tumer

Many cooperative multiagent reinforcement learning environments provide agents with a sparse team-based reward, as well as a dense agent-specific reward that incentivizes learning basic skills. Training policies solely on the team-based reward is often difficult due to its sparsity. Also, relying solely on the agent-specific reward is sub-optimal because it usually does not capture the team coordination objective. A common approach is to use reward shaping to construct a proxy reward by combining the individual rewards. However, this requires manual tuning for each environment. We introduce Multiagent Evolutionary Reinforcement Learning (MERL), a split-level training platform that handles the two objectives separately through two optimization processes. An evolutionary algorithm maximizes the sparse team-based objective through neuroevolution on a population of teams. Concurrently, a gradient-based optimizer trains policies to only maximize the dense agent-specific rewards. The gradient-based policies are periodically added to the evolutionary population as a way of information transfer between the two optimization processes. This enables the evolutionary algorithm to use skills learned via the agent-specific rewards toward optimizing the global objective. Results demonstrate that MERL significantly outperforms state-of-the-art methods, such as MADDPG, on a number of difficult coordination benchmarks.

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