A Multi-Agent system for Multi-Objective constrained optimization

2026-06-18

AI Summary

This work addresses the challenge in dynamic environments where existing reinforcement learning methods rely on manually specified reward weights, hindering their ability to adaptively balance primary objective optimization with constraint satisfaction. The authors propose MAMO, a novel approach that, for the first time, formulates reward weight selection as a learnable task. By leveraging multi-agent reinforcement learning, MAMO decouples task execution from objective design. The method integrates Lagrangian-inspired reward shaping with online policy learning to automatically adjust the trade-off between cost minimization and performance constraints. Evaluated in non-stationary settings, MAMO significantly enhances policy adaptability, robustness, and adherence to constraints without requiring manual tuning of reward coefficients.

Abstract

Many decision-making problems in computing and networking systems can be naturally formulated as cost-minimization problems under performance constraints. In dynamic environments, reinforcement learning (RL) is often used to solve such problems at runtime by embedding both costs and constraint violations into a single scalar reward through weighted penalty terms, following a Lagrangian-inspired formulation. However, in this context the behavior of the learned policy critically depends on the choice of these weights, which are typically selected manually. This makes it difficult to identify an appropriate trade-off between optimizing the primary objective and effectively avoiding constraint violations, particularly in non-stationary environments where their relative importance may change. This paper presents MAMO (Multi-Agent system for Multi-Objective constrained optimization), an approach to tackle this balancing problem through multi-agent RL. MAMO decouples task execution from objective design by formulating the selection of reward weights as a learning problem, providing a !rst step towards more autonomous and robust RL-based solutions for constrained optimization problems in dynamic environments.

Problem

• Multi-Agent Reinforcement Learning
• Constrained Optimization
• Reward Weight Tuning
• Dynamic Environments
• Multi-Objective Optimization

Innovation

• Multi-Agent Reinforcement Learning
• Constrained Optimization
• Reward Weight Learning
• Dynamic Environments
• Lagrangian Relaxation