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Efficient allocation is important in nature and human society, where individuals frequently compete for limited resources. The Minority Game (MG) is perhaps the simplest toy model to address this issue. However, most previous solutions…

Physics and Society · Physics 2026-02-04 Guozhong Zheng , Weiran Cai , Guanxiao Qi , Jiqiang Zhang , Li Chen

In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…

Optimization and Control · Mathematics 2021-03-05 Ather Gattami , Qinbo Bai , Vaneet Agarwal

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate…

Machine Learning · Computer Science 2025-09-30 Qi Lei , Sai Ganesh Nagarajan , Ioannis Panageas , Xiao Wang

Group Relative Policy Optimization (GRPO) has been shown to be an effective algorithm when an accurate reward model is available. However, such a highly reliable reward model is not available in many real-world tasks. In this paper, we…

Machine Learning · Computer Science 2026-01-12 Yuki Ichihara , Yuu Jinnai , Tetsuro Morimura , Mitsuki Sakamoto , Ryota Mitsuhashi , Eiji Uchibe

One of the fundamental challenges for offline reinforcement learning (RL) is ensuring robustness to data distribution. Whether the data originates from a near-optimal policy or not, we anticipate that an algorithm should demonstrate its…

Machine Learning · Computer Science 2023-10-18 Xiaohan Hu , Yi Ma , Chenjun Xiao , Yan Zheng , Jianye Hao

Multi-task reinforcement learning (RL) aims to find a single policy that effectively solves multiple tasks at the same time. This paper presents a constrained formulation for multi-task RL where the goal is to maximize the average…

Optimization and Control · Mathematics 2024-05-07 Sihan Zeng , Thinh T. Doan , Justin Romberg

Reinforcement learning with multiple, potentially conflicting objectives is pervasive in real-world applications, while this problem remains theoretically under-explored. This paper tackles the multi-objective reinforcement learning (MORL)…

Machine Learning · Computer Science 2024-05-10 Tianchen Zhou , FNU Hairi , Haibo Yang , Jia Liu , Tian Tong , Fan Yang , Michinari Momma , Yan Gao

Reinforcement learning (RL) is a framework to optimize a control policy using rewards that are revealed by the system as a response to a control action. In its standard form, RL involves a single agent that uses its policy to accomplish a…

Systems and Control · Electrical Eng. & Systems 2021-11-24 Juan Cervino , Juan Andres Bazerque , Miguel Calvo-Fullana , Alejandro Ribeiro

Under mild regularity conditions, gradient-based methods converge globally to a critical point in the single-loss setting. This is known to break down for vanilla gradient descent when moving to multi-loss optimization, but can we hope to…

Optimization and Control · Mathematics 2021-01-19 Alistair Letcher

In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…

Computer Science and Game Theory · Computer Science 2021-10-19 Yu-Guan Hsieh , Kimon Antonakopoulos , Panayotis Mertikopoulos

Reinforcement learning (RL) is a valuable tool for the creation of AI systems. However it may be problematic to adequately align RL based on scalar rewards if there are multiple conflicting values or stakeholders to be considered. Over the…

Machine Learning · Computer Science 2024-10-16 Peter Vamplew , Conor F Hayes , Cameron Foale , Richard Dazeley , Hadassah Harland

This paper addresses a critical societal consideration in the application of Reinforcement Learning (RL): ensuring equitable outcomes across different demographic groups in multi-task settings. While previous work has explored fairness in…

Machine Learning · Computer Science 2025-03-12 Kefan Song , Runnan Jiang , Rohan Chandra , Shangtong Zhang

We study the problem of Offline Safe Reinforcement Learning (OSRL), where the goal is to learn a reward-maximizing policy from fixed data under a cumulative cost constraint. We propose a novel OSRL approach that frames the problem as a…

Machine Learning · Computer Science 2025-10-28 Yassine Chemingui , Aryan Deshwal , Alan Fern , Thanh Nguyen-Tang , Janardhan Rao Doppa

Real-world decision-making tasks are generally complex, requiring trade-offs between multiple, often conflicting, objectives. Despite this, the majority of research in reinforcement learning and decision-theoretic planning either assumes…

Reinforcement learning (RL) has significantly advanced the control of physics-based and robotic characters that track kinematic reference motion. However, methods typically rely on a weighted sum of conflicting reward functions, requiring…

Robotics · Computer Science 2025-05-30 Lucas N. Alegre , Agon Serifi , Ruben Grandia , David Müller , Espen Knoop , Moritz Bächer

We present one of the first algorithms on model based reinforcement learning and trajectory optimization with free final time horizon. Grounded on the optimal control theory and Dynamic Programming, we derive a set of backward differential…

Systems and Control · Computer Science 2015-09-04 Wei Sun , Evangelos Theodorou , Panagiotis Tsiotras

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

Optimization and Control · Mathematics 2015-02-03 Julien Mairal

Reinforcement learning has achieved great success in many decision-making tasks, and traditional reinforcement learning algorithms are mainly designed for obtaining a single optimal solution. However, recent works show the importance of…

Machine Learning · Computer Science 2023-08-24 Fanqi Lin , Shiyu Huang , Weiwei Tu

Offline reinforcement learning (RL) defines the task of learning from a fixed batch of data. Due to errors in value estimation from out-of-distribution actions, most offline RL algorithms take the approach of constraining or regularizing…

Machine Learning · Computer Science 2021-12-06 Scott Fujimoto , Shixiang Shane Gu

Recently, a deep reinforcement learning method is proposed to solve multiobjective optimization problem. In this method, the multiobjective optimization problem is decomposed to a number of single-objective optimization subproblems and all…

Neural and Evolutionary Computing · Computer Science 2020-02-14 Hong Wu , Jiahai Wang , Zizhen Zhang