Stephen McAleer

Geunwoo Kim, Pierre Baldi, Stephen McAleer

Agents capable of carrying out general tasks on a computer can improve efficiency and productivity by automating repetitive tasks and assisting in complex problem-solving. Ideally, such agents should be able to solve new computer tasks presented to them through natural language commands. However, previous approaches to this problem require large amounts of expert demonstrations and task-specific reward functions, both of which are impractical for new tasks. In this work, we show that a pre-trained large language model (LLM) agent can execute computer tasks guided by natural language using a simple prompting scheme where the agent Recursively Criticizes and Improves its output (RCI). The RCI approach significantly outperforms existing LLM methods for automating computer tasks and surpasses supervised learning (SL) and reinforcement learning (RL) approaches on the MiniWoB++ benchmark. We compare multiple LLMs and find that RCI with the InstructGPT-3+RLHF LLM is state-of-the-art on MiniWoB++, using only a handful of demonstrations per task rather than tens of thousands, and without a task-specific reward function. Furthermore, we demonstrate RCI prompting's effectiveness in enhancing LLMs' reasoning abilities on a suite of natural language reasoning tasks, outperforming chain of thought (CoT) prompting with external feedback. We find that RCI combined with CoT performs better than either separately. Our code can be found here: https://github.com/posgnu/rci-agent.

Litian Liang, Yaosheng Xu, Stephen McAleer et al.

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.

Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster et al. · cambridge

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 open base 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 further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Julien Perolat, Bart de Vylder, Daniel Hennes et al.

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.

Jing Yu Koh, Stephen McAleer, Daniel Fried et al. · cmu

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 highlight the effectiveness of search for web agents, and we demonstrate that performance scales with increased test-time compute. We conduct a thorough analysis of our results to highlight improvements from search, limitations, and promising directions for future work. Our code and models are publicly released at https://jykoh.com/search-agents.

Ted Moskovitz, Aaditya K. Singh, DJ Strouse et al.

Large language models are typically aligned with human preferences by optimizing $\textit{reward models}$ (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 $\textit{overoptimization}$, wherein past a certain point, accumulating higher reward is associated with worse human ratings. In this paper, we perform, to our knowledge, 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 expressed by 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.

Lukas Schäfer, Oliver Slumbers, Stephen McAleer et al. · microsoft-research

Multi-agent reinforcement learning (MARL) requires agents to explore within a vast joint action space to find joint actions that lead to coordination. Existing value-based MARL algorithms commonly rely on random exploration, such as $ε$-greedy, to explore the environment which is not systematic and inefficient at identifying effective actions in multi-agent problems. Additionally, the concurrent training of the policies of multiple agents during training can render the optimisation non-stationary. This can lead to unstable value estimates, highly variant gradients, and ultimately hinder coordination between agents. To address these challenges, we propose ensemble value functions for multi-agent exploration (EMAX). EMAX is a framework to seamlessly extend value-based MARL algorithms. EMAX leverages an ensemble of value functions for each agent to guide their exploration, reduce the variance of their optimisation, and makes their policies more robust to miscoordination. EMAX achieves these benefits by (1) systematically guiding the exploration of agents with a UCB policy towards parts of the environment that require multiple agents to coordinate. (2) EMAX computes average value estimates across the ensemble as target values to reduce the variance of gradients and make optimisation more stable. (3) During evaluation, EMAX selects actions following a majority vote across the ensemble to reduce the likelihood of miscoordination. We first instantiate independent DQN with EMAX and evaluate it in 11 general-sum tasks with sparse rewards. We show that EMAX improves final evaluation returns by 185% across all tasks. We then evaluate EMAX on top of IDQN, VDN and QMIX in 21 common-reward tasks, and show that EMAX improves sample efficiency and final evaluation returns across all tasks over all three vanilla algorithms by 60%, 47%, and 538%, respectively.

Stephen McAleer, JB Lanier, Kevin Wang et al.

In competitive two-agent environments, deep reinforcement learning (RL) methods based on the \emph{Double Oracle (DO)} algorithm, such as \emph{Policy Space Response Oracles (PSRO)} and \emph{Anytime PSRO (APSRO)}, iteratively add RL best response policies to a population. Eventually, an optimal mixture of these population policies will approximate a Nash equilibrium. However, these methods might need to add all deterministic policies before converging. In this work, we introduce \emph{Self-Play PSRO (SP-PSRO)}, a method that adds an approximately optimal stochastic policy to the population in each iteration. Instead of adding only deterministic best responses to the opponent's least exploitable population mixture, SP-PSRO also learns an approximately optimal stochastic policy and adds it to the population as well. As a result, SP-PSRO empirically tends to converge much faster than APSRO and in many games converges in just a few iterations.

Stephen McAleer, Gabriele Farina, Marc Lanctot et al.

Recent techniques for approximating Nash equilibria in very large games leverage neural networks to learn approximately optimal policies (strategies). One promising 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.

JB Lanier, Stephen McAleer, Pierre Baldi et al.

Robust reinforcement learning (RL) considers the problem of learning policies that perform well in the worst case among a set of possible environment parameter values. In real-world environments, choosing the set of possible values for robust RL can be a difficult task. When that set is specified too narrowly, the agent will be left vulnerable to reasonable parameter values unaccounted for. When specified too broadly, the agent will be too cautious. In this paper, we propose Feasible Adversarial Robust RL (FARR), a novel problem formulation and objective for automatically determining the set of environment parameter values over which to be robust. FARR implicitly defines the set of feasible parameter values as those on which an agent could achieve a benchmark reward given enough training resources. By formulating this problem as a two-player zero-sum game, optimizing the FARR objective jointly produces an adversarial distribution over parameter values with feasible support and a policy robust over this feasible parameter set. We demonstrate that approximate Nash equilibria for this objective can be found using a variation of the PSRO algorithm. Furthermore, we show that an optimal agent trained with FARR is more robust to feasible adversarial parameter selection than with existing minimax, domain-randomization, and regret objectives in a parameterized gridworld and three MuJoCo control environments.

Jiaming Ji, Tianyi Qiu, Boyuan Chen et al.

AI alignment aims to make AI systems behave in line with human intentions and values. As AI systems grow more capable, so do risks from misalignment. To provide a comprehensive and up-to-date overview of the alignment field, in this survey, we delve into the core concepts, methodology, and practice of alignment. First, we identify four principles as the key objectives of AI alignment: Robustness, Interpretability, Controllability, and Ethicality (RICE). Guided by these four principles, we outline the landscape of current alignment research and decompose them into two key components: forward alignment and backward alignment. The former aims to make AI systems aligned via alignment training, while the latter aims to gain evidence about the systems' alignment and govern them appropriately to avoid exacerbating misalignment risks. On forward alignment, we discuss techniques for learning from feedback and learning under distribution shift. On backward alignment, we discuss assurance techniques and governance practices. We also release and continually update the website (www.alignmentsurvey.com) which features tutorials, collections of papers, blog posts, and other resources.

Jian Yao, Weiming Liu, Haobo Fu et al.

Policy-Space Response Oracles (PSRO) is an influential algorithm framework for approximating a Nash Equilibrium (NE) in multi-agent non-transitive games. Many previous studies have been trying to promote policy diversity in PSRO. A major weakness in existing diversity metrics is that a more diverse (according to their diversity metrics) population does not necessarily mean (as we proved in the paper) a better approximation to a NE. To alleviate this problem, we propose a new diversity metric, the improvement of which guarantees a better approximation to a NE. Meanwhile, we develop a practical and well-justified method to optimize our diversity metric using only state-action samples. By incorporating our diversity regularization into the best response solving in PSRO, we obtain a new PSRO variant, Policy Space Diversity PSRO (PSD-PSRO). We present the convergence property of PSD-PSRO. Empirically, extensive experiments on various games demonstrate that PSD-PSRO is more effective in producing significantly less exploitable policies than state-of-the-art PSRO variants.

Luke Marris, Marc Lanctot, Ian Gemp et al.

Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies have been used to rate strategies (e.g. Elo), however recent work has expanded ratings to utilize game theoretic solutions to better rate strategies in non-transitive games. This work generalizes these ideas and proposes novel algorithms suitable for N-player, general-sum rating of strategies in normal-form games according to the payoff rating system. This enables well-established solution concepts, such as equilibria, to be leveraged to efficiently rate strategies in games with complex strategic interactions, which arise in multiagent training and real-world interactions between many agents. We empirically validate our methods on real world normal-form data (Premier League) and multiagent reinforcement learning agent evaluation.

Chenguang Wang, Zhouliang Yu, Stephen McAleer et al.

Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.

Yongyuan Liang, Yanchao Sun, Ruijie Zheng et al.

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.

Yang Li, Kun Xiong, Yingping Zhang et al.

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 \url{https://sites.google.com/view/jiangjun-site/}.

Tim Franzmeyer, Stephen McAleer, João F. Henriques et al.

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 detectable using automated means or human inspection. Detectability is undesirable to adversaries as it may trigger security escalations. We introduce ε-illusory, a novel form of adversarial attack on sequential decision-makers that is both effective and of ε-bounded statistical detectability. We propose a novel dual ascent algorithm to learn such attacks end-to-end. Compared to existing attacks, we empirically find ε-illusory to be significantly harder to detect with automated methods, and a small study with human participants (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.

Yue Wu, Yewen Fan, So Yeon Min et al. · cmu

We propose an intuitive LLM prompting framework (AgentKit) for multifunctional agents. AgentKit offers a unified framework for explicitly constructing a complex "thought process" from simple natural language prompts. The basic building block in AgentKit is a node, containing a natural language prompt for a specific subtask. The user then puts together chains of nodes, like stacking LEGO pieces. The chains of nodes can be designed to explicitly enforce a naturally structured "thought process". For example, for the task of writing a paper, one may start with the thought process of 1) identify a core message, 2) identify prior research gaps, etc. The nodes in AgentKit can be designed and combined in different ways to implement multiple advanced capabilities including on-the-fly hierarchical planning, reflection, and learning from interactions. In addition, due to the modular nature and the intuitive design to simulate explicit human thought process, a basic agent could be implemented as simple as a list of prompts for the subtasks and therefore could be designed and tuned by someone without any programming experience. Quantitatively, we show that agents designed through AgentKit achieve SOTA performance on WebShop and Crafter. These advances underscore AgentKit's potential in making LLM agents effective and accessible for a wider range of applications. https://github.com/holmeswww/AgentKit

Stephen McAleer, John Lanier, Kevin Wang et al.

Policy Space Response Oracles (PSRO) is a reinforcement learning (RL) algorithm for two-player zero-sum games that has been empirically shown to find approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to an approximate Nash equilibrium and can handle continuous actions, it may take an exponential number of iterations as the number of information states (infostates) grows. We propose Extensive-Form Double Oracle (XDO), an extensive-form double oracle algorithm for two-player zero-sum games that is guaranteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations an order of magnitude smaller than PSRO. Experiments on a modified Leduc poker game and Oshi-Zumo show that tabular XDO achieves a lower exploitability than CFR with the same amount of computation. We also find that NXDO outperforms PSRO and NFSP on a sequential multidimensional continuous-action game. NXDO is the first deep RL method that can find an approximate Nash equilibrium in high-dimensional continuous-action sequential games. Experiment code is available at https://github.com/indylab/nxdo.

Stephen McAleer, John Lanier, Roy Fox et al.

Finding approximate Nash equilibria in zero-sum imperfect-information games is challenging when the number of information states is large. Policy Space Response Oracles (PSRO) is a deep reinforcement learning algorithm grounded in game theory that is guaranteed to converge to an approximate Nash equilibrium. However, PSRO requires training a reinforcement learning policy at each iteration, making it too slow for large games. We show through counterexamples and experiments that DCH and Rectified PSRO, two existing approaches to scaling up PSRO, fail to converge even in small games. We introduce Pipeline PSRO (P2SRO), the first scalable general method for finding approximate Nash equilibria in large zero-sum imperfect-information games. P2SRO is able to parallelize PSRO with convergence guarantees by maintaining a hierarchical pipeline of reinforcement learning workers, each training against the policies generated by lower levels in the hierarchy. We show that unlike existing methods, P2SRO converges to an approximate Nash equilibrium, and does so faster as the number of parallel workers increases, across a variety of imperfect information games. We also introduce an open-source environment for Barrage Stratego, a variant of Stratego with an approximate game tree complexity of $10^{50}$. P2SRO is able to achieve state-of-the-art performance on Barrage Stratego and beats all existing bots. Experiment code is available athttps://github.com/JBLanier/pipeline-psro.

Ariyan Bighashdel, Yongzhao Wang, Stephen McAleer et al.

Game theory provides a mathematical way to study the interaction between multiple decision makers. However, classical game-theoretic analysis is limited in scalability due to the large number of strategies, precluding direct application to more complex scenarios. This survey provides a comprehensive overview of a framework for large games, known as Policy Space Response Oracles (PSRO), which holds promise to improve scalability by focusing attention on sufficient subsets of strategies. We first motivate PSRO and provide historical context. We then focus on the strategy exploration problem for PSRO: the challenge of assembling effective subsets of strategies that still represent the original game well with minimum computational cost. We survey current research directions for enhancing the efficiency of PSRO, and explore the applications of PSRO across various domains. We conclude by discussing open questions and future research.

Pengdeng Li, Shuxin Li, Xinrun Wang et al.

Pursuit-evasion games (PEGs) model interactions between a team of pursuers and an evader in graph-based environments such as urban street networks. Recent advancements have demonstrated the effectiveness of the pre-training and fine-tuning paradigm in PSRO to improve scalability in solving large-scale PEGs. However, these methods primarily focus on specific PEGs with fixed initial conditions that may vary substantially in real-world scenarios, which significantly hinders the applicability of the traditional methods. To address this issue, we introduce Grasper, a GeneRAlist purSuer for Pursuit-Evasion pRoblems, capable of efficiently generating pursuer policies tailored to specific PEGs. Our contributions are threefold: First, we present a novel architecture that offers high-quality solutions for diverse PEGs, comprising critical components such as (i) a graph neural network (GNN) to encode PEGs into hidden vectors, and (ii) a hypernetwork to generate pursuer policies based on these hidden vectors. As a second contribution, we develop an efficient three-stage training method involving (i) a pre-pretraining stage for learning robust PEG representations through self-supervised graph learning techniques like GraphMAE, (ii) a pre-training stage utilizing heuristic-guided multi-task pre-training (HMP) where heuristic-derived reference policies (e.g., through Dijkstra's algorithm) regularize pursuer policies, and (iii) a fine-tuning stage that employs PSRO to generate pursuer policies on designated PEGs. Finally, we perform extensive experiments on synthetic and real-world maps, showcasing Grasper's significant superiority over baselines in terms of solution quality and generalizability. We demonstrate that Grasper provides a versatile approach for solving pursuit-evasion problems across a broad range of scenarios, enabling practical deployment in real-world situations.

Paul Friedrich, Yulun Zhang, Michael Curry et al. · cmu

Multi-Agent Path Finding (MAPF) involves determining paths for multiple agents to travel simultaneously and collision-free through a shared area toward given goal locations. This problem is computationally complex, especially when dealing with large numbers of agents, as is common in realistic applications like autonomous vehicle coordination. Finding an optimal solution is often computationally infeasible, making the use of approximate, suboptimal algorithms essential. Adding to the complexity, agents might act in a self-interested and strategic way, possibly misrepresenting their goals to the MAPF algorithm if it benefits them. Although the field of mechanism design offers tools to align incentives, using these tools without careful consideration can fail when only having access to approximately optimal outcomes. In this work, we introduce the problem of scalable mechanism design for MAPF and propose three strategyproof mechanisms, two of which even use approximate MAPF algorithms. We test our mechanisms on realistic MAPF domains with problem sizes ranging from dozens to hundreds of agents. We find that they improve welfare beyond a simple baseline.

Stephen McAleer, Kevin Wang, John Lanier et al.

Policy space response oracles (PSRO) is a multi-agent reinforcement learning algorithm that has achieved state-of-the-art performance in very large two-player zero-sum games. PSRO is based on the tabular double oracle (DO) method, an algorithm that is guaranteed to converge to a Nash equilibrium, but may increase exploitability from one iteration to the next. We propose anytime double oracle (ADO), a tabular double oracle algorithm for 2-player zero-sum games that is guaranteed to converge to a Nash equilibrium while decreasing exploitability from one iteration to the next. Unlike DO, in which the restricted distribution is based on the restricted game formed by each player's strategy sets, ADO finds the restricted distribution for each player that minimizes its exploitability against any policy in the full, unrestricted game. We also propose a method of finding this restricted distribution via a no-regret algorithm updated against best responses, called RM-BR DO. Finally, we propose anytime PSRO (APSRO), a version of ADO that calculates best responses via reinforcement learning. In experiments on Leduc poker and random normal form games, we show that our methods achieve far lower exploitability than DO and PSRO and decrease exploitability monotonically.

Yaosheng Xu, Dailin Hu, Litian Liang et al.

Soft Actor-Critic (SAC) is considered the state-of-the-art algorithm in continuous action space settings. It uses the maximum entropy framework for efficiency and stability, and applies a heuristic temperature Lagrange term to tune the temperature $α$, which determines how "soft" the policy should be. It is counter-intuitive that empirical evidence shows SAC does not perform well in discrete domains. In this paper we investigate the possible explanations for this phenomenon and propose Target Entropy Scheduled SAC (TES-SAC), an annealing method for the target entropy parameter applied on SAC. Target entropy is a constant in the temperature Lagrange term and represents the target policy entropy in discrete SAC. We compare our method on Atari 2600 games with different constant target entropy SAC, and analyze on how our scheduling affects SAC.

Litian Liang, Yaosheng Xu, Stephen McAleer et al.

Temporal-Difference (TD) learning methods, such as Q-Learning, have proven effective at learning a policy to perform control tasks. One issue with methods like Q-Learning is that the value update introduces bias when predicting the TD target of a unfamiliar state. Estimation noise becomes a bias after the max operator in the policy improvement step, and carries over to value estimations of other states, causing Q-Learning to overestimate the Q value. Algorithms like Soft Q-Learning (SQL) introduce the notion of a soft-greedy policy, which reduces the estimation bias via soft updates in early stages of training. However, the inverse temperature $β$ that controls the softness of an update is usually set by a hand-designed heuristic, which can be inaccurate at capturing the uncertainty in the target estimate. Under the belief that $β$ is closely related to the (state dependent) model uncertainty, Entropy Regularized Q-Learning (EQL) further introduces a principled scheduling of $β$ by maintaining a collection of the model parameters that characterizes model uncertainty. In this paper, we present Unbiased Soft Q-Learning (UQL), which extends the work of EQL from two action, finite state spaces to multi-action, infinite state space Markov Decision Processes. We also provide a principled numerical scheduling of $β$, extended from SQL and using model uncertainty, during the optimization process. We show the theoretical guarantees and the effectiveness of this update method in experiments on several discrete control environments.

Roy Fox, Stephen McAleer, Will Overman et al.

Multi-agent reinforcement learning has been successfully applied to fully-cooperative and fully-competitive environments, but little is currently known about mixed cooperative/competitive environments. In this paper, we focus on a particular class of multi-agent mixed cooperative/competitive stochastic games called Markov Potential Games (MPGs), which include cooperative games as a special case. Recent results have shown that independent policy gradient converges in MPGs but it was not known whether Independent Natural Policy Gradient converges in MPGs as well. We prove that Independent Natural Policy Gradient always converges in the last iterate using constant learning rates. The proof deviates from the existing approaches and the main challenge lies in the fact that Markov Potential Games do not have unique optimal values (as single-agent settings exhibit) so different initializations can lead to different limit point values. We complement our theoretical results with experiments that indicate that Natural Policy Gradient outperforms Policy Gradient in routing games and congestion games.

Stephen McAleer, John Lanier, Michael Dennis et al.

Machine learning algorithms often make decisions on behalf of agents with varied and sometimes conflicting interests. In domains where agents can choose to take their own action or delegate their action to a central mediator, an open question is how mediators should take actions on behalf of delegating agents. The main existing approach uses delegating agents to punish non-delegating agents in an attempt to get all agents to delegate, which tends to be costly for all. We introduce a Pareto Mediator which aims to improve outcomes for delegating agents without making any of them worse off. Our experiments in random normal form games, a restaurant recommendation game, and a reinforcement learning sequential social dilemma show that the Pareto Mediator greatly increases social welfare. Also, even when the Pareto Mediator is based on an incorrect model of agent utility, performance gracefully degrades to the pre-intervention level, due to the individual autonomy preserved by the voluntary mediator.

Xidong Feng, Oliver Slumbers, Ziyu Wan et al.

When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent population. Within such a process, the update rules of "who to compete with" (i.e., the opponent mixture) and "how to beat them" (i.e., finding best responses) are underpinned by manually developed game theoretical principles such as fictitious play and Double Oracle. In this paper, we introduce a novel framework -- Neural Auto-Curricula (NAC) -- that leverages meta-gradient descent to automate the discovery of the learning update rule without explicit human design. Specifically, we parameterise the opponent selection module by neural networks and the best-response module by optimisation subroutines, and update their parameters solely via interaction with the game engine, where both players aim to minimise their exploitability. Surprisingly, even without human design, the discovered MARL algorithms achieve competitive or even better performance with the state-of-the-art population-based game solvers (e.g., PSRO) on Games of Skill, differentiable Lotto, non-transitive Mixture Games, Iterated Matching Pennies, and Kuhn Poker. Additionally, we show that NAC is able to generalise from small games to large games, for example training on Kuhn Poker and outperforming PSRO on Leduc Poker. Our work inspires a promising future direction to discover general MARL algorithms solely from data.

Le Cong Dinh, Yaodong Yang, Stephen McAleer et al.

Solving strategic games with huge action space 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) methods from game theory. Our method -- \emph{Online Double Oracle (ODO)} -- is provably convergent to a Nash equilibrium (NE). Most importantly, unlike normal DO methods, ODO is \emph{rationale} in the sense that each agent in ODO can exploit strategic adversary with a regret bound of $\mathcal{O}(\sqrt{T k \log(k)})$ where $k$ is not the total number of pure strategies, but rather the size of \emph{effective strategy set} that is linearly dependent on the support size of the NE. On tens of different real-world games, ODO outperforms DO, PSRO methods, and no-regret algorithms such as Multiplicative Weight Update by a significant margin, both in terms of convergence rate to a NE and average payoff against strategic adversaries.

Forest Agostinelli, Shahaf S. Shperberg, Alexander Shmakov et al.

Efficiently solving problems with large action spaces using A* search remains a significant challenge. This is because, for each iteration of A* search, the number of nodes generated and the number of heuristic function applications 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 issue, we introduce Q*, a search algorithm that leverages heuristics capable of receiving a state and, in a single function call, returning cost-to-go estimates for all possible transitions from that state, along with estimates of the corresponding transition costs -- without the need to apply the transitions or generate the successor states; such action-state estimation are typically known as Q-values. This significantly reduces computation time and memory usage. In addition, we prove that Q* search is guaranteed to find a shortest path given a heuristic function that does not overestimate the sum of the transition cost and cost-to-go of the state. To obtain heuristics for Q* search, we employ a deep Q-network architecture to learn a state-action heuristic function from domain interaction, without any prior knowledge. We use Q* with our learned heuristic on different domains and action spaces, showing that Q* suffers from only a small runtime overhead as the size of the action space 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.

Stephen McAleer, Alex Fast, Yuntian Xue et al.

Two-photon excitation fluorescence (2PEF) allows imaging of tissue up to about one millimeter in thickness. Typically, reducing fluorescence excitation exposure reduces the quality of the image. However, using deep learning super resolution techniques, these low-resolution images can be converted to high-resolution images. This work explores improving human tissue imaging by applying deep learning to maximize image quality while reducing fluorescence excitation exposure. We analyze two methods: a method based on U-Net, and a patch-based regression method. Both methods are evaluated on a skin dataset and an eye dataset. The eye dataset includes 1200 paired high power and low power images of retinal organoids. The skin dataset contains multiple frames of each sample of human skin. High-resolution images were formed by averaging 70 frames for each sample and low-resolution images were formed by averaging the first 7 and 15 frames for each sample. The skin dataset includes 550 images for each of the resolution levels. We track two measures of performance for the two methods: mean squared error (MSE) and structural similarity index measure (SSIM). For the eye dataset, the patches method achieves an average MSE of 27,611 compared to 146,855 for the U-Net method, and an average SSIM of 0.636 compared to 0.607 for the U-Net method. For the skin dataset, the patches method achieves an average MSE of 3.768 compared to 4.032 for the U-Net method, and an average SSIM of 0.824 compared to 0.783 for the U-Net method. Despite better performance on image quality, the patches method is worse than the U-Net method when comparing the speed of prediction, taking 303 seconds to predict one image compared to less than one second for the U-Net method.

Yaodong Yang, Chengdong Ma, Zihan Ding et al.

Tremendous advances have been made in multiagent reinforcement learning (MARL). MARL corresponds to the learning problem in a multiagent system in which multiple agents learn simultaneously. It is an interdisciplinary field of study with a long history that includes game theory, machine learning, stochastic control, psychology, and optimization. Despite great successes in MARL, there is a lack of a self-contained overview of the literature that covers game-theoretic foundations of modern MARL methods and summarizes the recent advances. The majority of existing surveys are outdated and do not fully cover the recent developments since 2010. In this work, we provide a monograph on MARL that covers both the fundamentals and the latest developments on the research frontier. The goal of this monograph is to provide a self-contained assessment of the current state-of-the-art MARL techniques from a game-theoretic perspective. We expect this work to serve as a stepping stone for both new researchers who are about to enter this fast-growing field and experts in the field who want to obtain a panoramic view and identify new directions based on recent advances.

Shauharda Khadka, Somdeb Majumdar, Santiago Miret et al.

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. Furthermore, 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.

John B. Lanier, Stephen McAleer, Pierre Baldi

Dealing with sparse rewards is a longstanding challenge in reinforcement learning. The recent use of hindsight methods have achieved success on a variety of sparse-reward tasks, but they fail on complex tasks such as stacking multiple blocks with a robot arm in simulation. Curiosity-driven exploration using the prediction error of a learned dynamics model as an intrinsic reward has been shown to be effective for exploring a number of sparse-reward environments. We present a method that combines hindsight with curiosity-driven exploration and curriculum learning in order to solve the challenging sparse-reward block stacking task. We are the first to stack more than two blocks using only sparse reward without human demonstrations.

Stephen McAleer, Forest Agostinelli, Alexander Shmakov et al.

A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman proficiency in Go, Chess, and Shogi without human data or domain knowledge. In these environments, a reward is always received at the end of the game, however, for many combinatorial optimization environments, rewards are sparse and episodes are not guaranteed to terminate. We introduce Autodidactic Iteration: a novel reinforcement learning algorithm that is able to teach itself how to solve the Rubik's Cube with no human assistance. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves -- less than or equal to solvers that employ human domain knowledge.