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In this paper, we use the multi-agent reinforcement learning (MARL) algorithm to find the generalized Nash equilibria (GNEs) of Generalized Nash Equilibrium problems (GNEPs). A GNEP is viewed as a partially observable Markov game (POMG) that can be solved iteratively through our proposed state dynamic and reward function using a MARL algorithm. To achieve our goals, we collect six test examples of GNEPs (four shared convex constraints and two non-shared convex constraints) that can be solved by classical numerical optimization methods (NOMs), like the Gauss-Seidel method (GSM) and the augmented Lagrangian method (ALM). As a MARL algorithm, we use the Multi-Agent Deep Deterministic Policy Gradient (MADDPG), which performs well in continuous environments. Our results show that MADDPG can efficiently solve GNEPs (shared and non-shared constraints) involving two and three players, achieving results comparable to classical NOMs and the Multi-Agent Proximal Policy Optimization (MAPPO), a well-known MARL algorithm. Additionally, MADDPG solves more GNEPs than MAPPO, even if neither can solve the high-dimensional GNEPs (e.g., the electricity market problem) that some NOMs have solved. Furthermore, we present these GNEPs as benchmark environments, which we believe are crucial for testing and evaluating the performance of MARL algorithms.

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Reinforcement Learning for Solving Generalized Nash Equilibrium Problem

  • 会议论文

  • 发表日期：

    2026年

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  • Benjamin Benteke Longaou,
  • Monica-Gabriela Cojocaru,
  • Nickolas Hoover

摘要

In this paper, we use the multi-agent reinforcement learning (MARL) algorithm to find the generalized Nash equilibria (GNEs) of Generalized Nash Equilibrium problems (GNEPs). A GNEP is viewed as a partially observable Markov game (POMG) that can be solved iteratively through our proposed state dynamic and reward function using a MARL algorithm. To achieve our goals, we collect six test examples of GNEPs (four shared convex constraints and two non-shared convex constraints) that can be solved by classical numerical optimization methods (NOMs), like the Gauss-Seidel method (GSM) and the augmented Lagrangian method (ALM). As a MARL algorithm, we use the Multi-Agent Deep Deterministic Policy Gradient (MADDPG), which performs well in continuous environments. Our results show that MADDPG can efficiently solve GNEPs (shared and non-shared constraints) involving two and three players, achieving results comparable to classical NOMs and the Multi-Agent Proximal Policy Optimization (MAPPO), a well-known MARL algorithm. Additionally, MADDPG solves more GNEPs than MAPPO, even if neither can solve the high-dimensional GNEPs (e.g., the electricity market problem) that some NOMs have solved. Furthermore, we present these GNEPs as benchmark environments, which we believe are crucial for testing and evaluating the performance of MARL algorithms.