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Balance Reward and Safety Optimization for Safe Reinforcement Learning: A Perspective of Gradient Manipulation

Shangding Gu, Bilgehan Sel, Yuhao Ding, Lu Wang, Qingwei Lin, Ming Jin, Alois Knoll

TL;DR

Balancing reward optimization and safety in CMDPs is challenging due to gradient conflicts between $V_r^ pi( ho)$ and $V_c^ pi( ho)$. The paper introduces Projection Constraint-Rectified Policy Optimization (PCRPO) with soft switching and a slack mechanism to manipulate reward and cost gradients, along with convergence guarantees. It provides a Safe Reinforcement Learning framework and two benchmarks (Safety-MuJoCo and Omnisafe) to evaluate performance, showing PCRPO outperforms state-of-the-art baselines in reward-safety trade-offs. The work delivers monotonic improvement guarantees and practical guidance for deploying safe RL in real-world tasks.

Abstract

Ensuring the safety of Reinforcement Learning (RL) is crucial for its deployment in real-world applications. Nevertheless, managing the trade-off between reward and safety during exploration presents a significant challenge. Improving reward performance through policy adjustments may adversely affect safety performance. In this study, we aim to address this conflicting relation by leveraging the theory of gradient manipulation. Initially, we analyze the conflict between reward and safety gradients. Subsequently, we tackle the balance between reward and safety optimization by proposing a soft switching policy optimization method, for which we provide convergence analysis. Based on our theoretical examination, we provide a safe RL framework to overcome the aforementioned challenge, and we develop a Safety-MuJoCo Benchmark to assess the performance of safe RL algorithms. Finally, we evaluate the effectiveness of our method on the Safety-MuJoCo Benchmark and a popular safe RL benchmark, Omnisafe. Experimental results demonstrate that our algorithms outperform several state-of-the-art baselines in terms of balancing reward and safety optimization.

Balance Reward and Safety Optimization for Safe Reinforcement Learning: A Perspective of Gradient Manipulation

TL;DR

Balancing reward optimization and safety in CMDPs is challenging due to gradient conflicts between and . The paper introduces Projection Constraint-Rectified Policy Optimization (PCRPO) with soft switching and a slack mechanism to manipulate reward and cost gradients, along with convergence guarantees. It provides a Safe Reinforcement Learning framework and two benchmarks (Safety-MuJoCo and Omnisafe) to evaluate performance, showing PCRPO outperforms state-of-the-art baselines in reward-safety trade-offs. The work delivers monotonic improvement guarantees and practical guidance for deploying safe RL in real-world tasks.

Abstract

Ensuring the safety of Reinforcement Learning (RL) is crucial for its deployment in real-world applications. Nevertheless, managing the trade-off between reward and safety during exploration presents a significant challenge. Improving reward performance through policy adjustments may adversely affect safety performance. In this study, we aim to address this conflicting relation by leveraging the theory of gradient manipulation. Initially, we analyze the conflict between reward and safety gradients. Subsequently, we tackle the balance between reward and safety optimization by proposing a soft switching policy optimization method, for which we provide convergence analysis. Based on our theoretical examination, we provide a safe RL framework to overcome the aforementioned challenge, and we develop a Safety-MuJoCo Benchmark to assess the performance of safe RL algorithms. Finally, we evaluate the effectiveness of our method on the Safety-MuJoCo Benchmark and a popular safe RL benchmark, Omnisafe. Experimental results demonstrate that our algorithms outperform several state-of-the-art baselines in terms of balancing reward and safety optimization.
Paper Structure (35 sections, 2 theorems, 57 equations, 8 figures, 5 tables, 1 algorithm)

This paper contains 35 sections, 2 theorems, 57 equations, 8 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Markov Decision Processes
  5. Constrained MDP
  6. Primal vs Primal-dual Approaches
  7. Method
  8. Soft Switching through Gradient Manipulation
  9. Gradient Analysis with Soft Switching
  10. A Framework for Safe Reinforcement Learning with Soft Switching
  11. Policy Evaluation
  12. Policy Improvement for Reward and Safety
  13. Correlation-Reduction for Stochastic Gradient Manipulation
  14. Comparison to CRPO
  15. Convergence Analysis
  16. ...and 20 more sections

Key Result

Theorem B.1

Under the assumption of Lipschitz continuity with a constant L, for the iterates $\pi_{w_t}$ generated through our gradient manipulation, when $180^\circ > \theta \geq 90^\circ$, as depicted in Equation(appendix-eq:upper-bound-lower-bound-theta-more-than-90-degree), both the upper and lower bounds o In the case of $180^\circ > \theta \geq 90^\circ$, the following property holds,

Figures (8)

  • Figure 1: Conflicts between reward and cost optimization.
  • Figure 2: Soft switching through gradient manipulation.
  • Figure 3: Analysis of Soft switching through gradient manipulation.
  • Figure 4: Compared with CRPO on the SafetyWalker and SafetyHumanoidStandup Tasks. To encourage more learning exploration, we initiate the optimization of safety after $640000$ steps.
  • Figure 5: Compared with PCPO, CUP, PPOLag baselines on SafetyHopperVelocity-v1 and SafetyAntVelocity-v1 tasks.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Theorem B.1
  • proof
  • Theorem B.2
  • proof