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DeepSafeMPC: Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning

Xuefeng Wang, Henglin Pu, Hyung Jun Kim, Husheng Li

TL;DR

DeepSafeMPC integrates a centralized deep learning predictor for implicit multi-agent dynamics with MAPPO and nonlinear Model Predictive Control to enforce safety constraints in multi-agent reinforcement learning. The framework uses MAPPO to explore policies, a deep predictor to forecast future states, and MPC (via SQP) to optimize actions over a horizon while respecting safety costs. Empirical results in Safe MAMuJoCo show that MPC refines actions to reduce unsafe behavior and costs, with prediction error decreasing to around 0.0015 over training. This work provides a practical, scalable method for achieving forward-looking safety in complex multi-agent environments.

Abstract

Safe Multi-agent reinforcement learning (safe MARL) has increasingly gained attention in recent years, emphasizing the need for agents to not only optimize the global return but also adhere to safety requirements through behavioral constraints. Some recent work has integrated control theory with multi-agent reinforcement learning to address the challenge of ensuring safety. However, there have been only very limited applications of Model Predictive Control (MPC) methods in this domain, primarily due to the complex and implicit dynamics characteristic of multi-agent environments. To bridge this gap, we propose a novel method called Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning (DeepSafeMPC). The key insight of DeepSafeMPC is leveraging a entralized deep learning model to well predict environmental dynamics. Our method applies MARL principles to search for optimal solutions. Through the employment of MPC, the actions of agents can be restricted within safe states concurrently. We demonstrate the effectiveness of our approach using the Safe Multi-agent MuJoCo environment, showcasing significant advancements in addressing safety concerns in MARL.

DeepSafeMPC: Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning

TL;DR

DeepSafeMPC integrates a centralized deep learning predictor for implicit multi-agent dynamics with MAPPO and nonlinear Model Predictive Control to enforce safety constraints in multi-agent reinforcement learning. The framework uses MAPPO to explore policies, a deep predictor to forecast future states, and MPC (via SQP) to optimize actions over a horizon while respecting safety costs. Empirical results in Safe MAMuJoCo show that MPC refines actions to reduce unsafe behavior and costs, with prediction error decreasing to around 0.0015 over training. This work provides a practical, scalable method for achieving forward-looking safety in complex multi-agent environments.

Abstract

Safe Multi-agent reinforcement learning (safe MARL) has increasingly gained attention in recent years, emphasizing the need for agents to not only optimize the global return but also adhere to safety requirements through behavioral constraints. Some recent work has integrated control theory with multi-agent reinforcement learning to address the challenge of ensuring safety. However, there have been only very limited applications of Model Predictive Control (MPC) methods in this domain, primarily due to the complex and implicit dynamics characteristic of multi-agent environments. To bridge this gap, we propose a novel method called Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning (DeepSafeMPC). The key insight of DeepSafeMPC is leveraging a entralized deep learning model to well predict environmental dynamics. Our method applies MARL principles to search for optimal solutions. Through the employment of MPC, the actions of agents can be restricted within safe states concurrently. We demonstrate the effectiveness of our approach using the Safe Multi-agent MuJoCo environment, showcasing significant advancements in addressing safety concerns in MARL.
Paper Structure (19 sections, 4 theorems, 19 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 19 sections, 4 theorems, 19 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. PRELIMINARIES
  4. Constrained Markov Decision Process
  5. Model Predictive Control
  6. METHODOLOGY
  7. Multi-Agent Proximal Policy Optimization
  8. Dynamics Predictor
  9. Integration with MPC
  10. Implementation
  11. EXPERIMENTAL RESULTS
  12. Safe Multi-Agent MuJoCo
  13. Metrics for Reinforcement Learning
  14. Cost Function
  15. Simulation Results
  16. ...and 4 more sections

Key Result

Lemma IV.1

If the conditions of Assumption ap:model_prediction hold, we have: where $\varepsilon_w > 0$, $\varepsilon_e > 0$, they represents the bound of distance between the optimal weights and actual weights and the distance between the outputs predictor generated by these two set of weights. Here, $\| \cdot \|$ denotes the $L_2$ norm.

Figures (5)

  • Figure 1: Implementation of DeepSafeMPC. This framework can be divided into RL and MPC parts. Within the RL domain, Policy Networks produce initial action vectors $\{\hat{a}^t_1, \hat{a}^t_2, \ldots, \hat{a}^t_n\}$. These vectors serve as preliminary inputs to the MPC's Predictor component and the initial guess for MPC optimizer. The Predictor, utilizing a Multi-Layer Perceptron (MLP), forecasts the forthcoming state $\hat{s} ^{t+1}$ based on the current state $s^t$ and action $\mathbf{a}^t$. Subsequently, the Optimizer refines these actions into an optimized sequence $\mathbf{a}^t = \{a^t_1, a^t_2, \ldots, a^t_n\}$ over the decision horizon $T$.
  • Figure 2: Experimental results: (a) Two-Agent Ant, (b) Half Cheetah, and (c) Swimmer.
  • Figure 3: Comparison between with and w/o MPC.
  • Figure 4: Prediction Error during Training.
  • Figure 5: Three environments in the experiments: (a) Two-Agent Ant, (b) Half Cheetah, and (c) Swimmer.

Theorems & Definitions (8)

  • Lemma IV.1
  • proof
  • Theorem IV.2
  • proof
  • Lemma IV.3
  • proof
  • Theorem IV.4
  • proof