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We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. We derive several new algorithms for dynamic programming and…

In today's rapidly evolving military landscape, advancing artificial intelligence (AI) in support of wargaming becomes essential. Despite reinforcement learning (RL) showing promise for developing intelligent agents, conventional RL faces…

Machine Learning · Computer Science 2024-08-27 Scotty Black

This paper studies the continuous-time q-learning in mean-field jump-diffusion models when the population distribution is not directly observable. We propose the integrated q-function in decoupled form (decoupled Iq-function) from the…

Optimization and Control · Mathematics 2025-03-24 Xiaoli Wei , Xiang Yu , Fengyi Yuan

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy…

Optimization and Control · Mathematics 2021-12-10 Xin Guo , Renyuan Xu , Thaleia Zariphopoulou

We propose a mean field control game model for the intra-and-inter-bank borrowing and lending problem. This framework allows to study the competitive game arising between groups of collaborative banks. The solution is provided in terms of…

Optimization and Control · Mathematics 2022-07-08 Andrea Angiuli , Nils Detering , Jean-Pierre Fouque , Mathieu Laurière , Jimin Lin

Multi-agent settings remain a fundamental challenge in the reinforcement learning (RL) domain due to the partial observability and the lack of accurate real-time interactions across agents. In this paper, we propose a new method based on…

Machine Learning · Computer Science 2023-01-03 Donghan Xie , Zhi Wang , Chunlin Chen , Daoyi Dong

In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field…

Machine Learning · Computer Science 2024-10-04 Jiawei Huang , Batuhan Yardim , Niao He

In the domain of continuous control, deep reinforcement learning (DRL) demonstrates promising results. However, the dependence of DRL on deep neural networks (DNNs) results in the demand for extensive data and increased computational cost.…

Machine Learning · Computer Science 2025-04-15 Shiron Thalagala , Pak Kin Wong , Xiaozheng Wang , Tianang Sun

Counterfactual regret minimization (CFR) is a popular method to deal with decision-making problems of two-player zero-sum games with imperfect information. Unlike existing studies that mostly explore for solving larger scale problems or…

Machine Learning · Computer Science 2020-09-15 Huale Li , Xuan Wang , Fengwei Jia , Yifan Li , Yulin Wu , Jiajia Zhang , Shuhan Qi

In this work, we propose, for the first time, a reinforcement learning framework specifically designed for zero-sum linear-quadratic stochastic differential games. This approach offers a generalized solution for scenarios in which accurate…

Optimization and Control · Mathematics 2026-02-10 Yiyuan Wang

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent…

Machine Learning · Computer Science 2019-10-10 Mridul Agarwal , Vaneet Aggarwal , Arnob Ghosh , Nilay Tiwari

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk,…

Mathematical Finance · Quantitative Finance 2025-05-16 Shanyu Han , Yang Liu , Xiang Yu

We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function,…

Machine Learning · Statistics 2023-03-14 Noufel Frikha , Maximilien Germain , Mathieu Laurière , Huyên Pham , Xuanye Song

Despite the fact that deep reinforcement learning (RL) has surpassed human-level performances in various tasks, it still has several fundamental challenges. First, most RL methods require intensive data from the exploration of the…

Machine Learning · Computer Science 2021-07-06 Zhe Xu , Bo Wu , Aditya Ojha , Daniel Neider , Ufuk Topcu

In this paper, we introduce a regularized mean-field game and study learning of this game under an infinite-horizon discounted reward function. Regularization is introduced by adding a strongly concave regularization function to the…

Optimization and Control · Mathematics 2022-11-11 Berkay Anahtarci , Can Deha Kariksiz , Naci Saldi

Mean Field Games (MFGs) have the ability to handle large-scale multi-agent systems, but learning Nash equilibria in MFGs remains a challenging task. In this paper, we propose a deep reinforcement learning (DRL) algorithm that achieves…

Computer Science and Game Theory · Computer Science 2024-03-07 Zida Wu , Mathieu Lauriere , Samuel Jia Cong Chua , Matthieu Geist , Olivier Pietquin , Ankur Mehta

Over the past decades, researchers have been pushing the limits of Deep Reinforcement Learning (DRL). Although DRL has attracted substantial interest from practitioners, many are blocked by having to search through a plethora of available…

Mathematical Finance · Quantitative Finance 2023-10-05 Sophia Gu

Reinforcement learning (RL) algorithms have been around for decades and employed to solve various sequential decision-making problems. These algorithms however have faced great challenges when dealing with high-dimensional environments. The…

Machine Learning · Computer Science 2020-04-01 Thanh Thi Nguyen , Ngoc Duy Nguyen , Saeid Nahavandi

We explore the problem of imitation learning (IL) in the context of mean-field games (MFGs), where the goal is to imitate the behavior of a population of agents following a Nash equilibrium policy according to some unknown payoff function.…

Machine Learning · Computer Science 2023-06-27 Giorgia Ramponi , Pavel Kolev , Olivier Pietquin , Niao He , Mathieu Laurière , Matthieu Geist

Methods like multi-agent reinforcement learning struggle to scale with growing population size. Mean-field games (MFGs) are a game-theoretic approach that can circumvent this by finding a solution for an abstract infinite population, which…

Multiagent Systems · Computer Science 2025-12-23 Patrick Benjamin , Alessandro Abate