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Safe and Balanced: A Framework for Constrained Multi-Objective Reinforcement Learning

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

TL;DR

This work tackles safe, multi-objective reinforcement learning by proposing a primal-based framework (CR-MOPO) that simultaneously optimizes multiple task objectives while enforcing hard safety constraints. The core innovation is a Conflict-Averse Natural Policy Gradient (CA-NPG) that mitigates gradient conflicts among objectives, coupled with a constraint-rectification mechanism to enforce safety when needed. The authors provide theoretical convergence and constraint-violation guarantees in the tabular setting and demonstrate superior performance over state-of-the-art baselines CRPO and LP3 on the Safe Multi-Objective MuJoCo benchmark. The approach yields monotonic improvements in objective rewards while maintaining safety, offering a practical pathway toward robust, safe MORL in complex control tasks.

Abstract

In numerous reinforcement learning (RL) problems involving safety-critical systems, a key challenge lies in balancing multiple objectives while simultaneously meeting all stringent safety constraints. To tackle this issue, we propose a primal-based framework that orchestrates policy optimization between multi-objective learning and constraint adherence. Our method employs a novel natural policy gradient manipulation method to optimize multiple RL objectives and overcome conflicting gradients between different tasks, since the simple weighted average gradient direction may not be beneficial for specific tasks' performance due to misaligned gradients of different task objectives. When there is a violation of a hard constraint, our algorithm steps in to rectify the policy to minimize this violation. We establish theoretical convergence and constraint violation guarantees in a tabular setting. Empirically, our proposed method also outperforms prior state-of-the-art methods on challenging safe multi-objective reinforcement learning tasks.

Safe and Balanced: A Framework for Constrained Multi-Objective Reinforcement Learning

TL;DR

This work tackles safe, multi-objective reinforcement learning by proposing a primal-based framework (CR-MOPO) that simultaneously optimizes multiple task objectives while enforcing hard safety constraints. The core innovation is a Conflict-Averse Natural Policy Gradient (CA-NPG) that mitigates gradient conflicts among objectives, coupled with a constraint-rectification mechanism to enforce safety when needed. The authors provide theoretical convergence and constraint-violation guarantees in the tabular setting and demonstrate superior performance over state-of-the-art baselines CRPO and LP3 on the Safe Multi-Objective MuJoCo benchmark. The approach yields monotonic improvements in objective rewards while maintaining safety, offering a practical pathway toward robust, safe MORL in complex control tasks.

Abstract

In numerous reinforcement learning (RL) problems involving safety-critical systems, a key challenge lies in balancing multiple objectives while simultaneously meeting all stringent safety constraints. To tackle this issue, we propose a primal-based framework that orchestrates policy optimization between multi-objective learning and constraint adherence. Our method employs a novel natural policy gradient manipulation method to optimize multiple RL objectives and overcome conflicting gradients between different tasks, since the simple weighted average gradient direction may not be beneficial for specific tasks' performance due to misaligned gradients of different task objectives. When there is a violation of a hard constraint, our algorithm steps in to rectify the policy to minimize this violation. We establish theoretical convergence and constraint violation guarantees in a tabular setting. Empirically, our proposed method also outperforms prior state-of-the-art methods on challenging safe multi-objective reinforcement learning tasks.
Paper Structure (23 sections, 11 theorems, 81 equations, 5 figures, 2 tables, 2 algorithms)

This paper contains 23 sections, 11 theorems, 81 equations, 5 figures, 2 tables, 2 algorithms.

Key Result

Theorem 5.2

Consider Algorithm alg:MOPO-CR in the tabular setting with softmax policy parameterization and any policy initialization $w_0 \in \mathcal{R}^{\left|\mathcal{S} \right| \left|\mathcal{A} \right|}$. Let the tolerance be $\beta = \mathcal{O} \left(\frac{m B_1 \sqrt{\left|\mathcal{S}\right| \left| \mat

Figures (5)

  • Figure 1: CR-MOPO on Safe Multi-Objective MuJoCo environments regarding the reward and safety performance.
  • Figure 2: (a) and (b) show two of the Safe Multi-Objective MuJoCO environments, Safe Multi-Objective Humanoid and Pusher. (c) and (d) show the comparison results in terms of CR-MOPO, CR-MOPO-S and CRPO xu2021crpo on a Safe Multi-Objective MuJoCo environment, Safe Multi-Objective HalfCheetah, the cost limit is $0.005$, we start to optimize safety violation after $40$ Epochs.
  • Figure 3: Compared with the DeepMind's method, LP3 huang2022constrained, on Safe Multi-Objective Walker-dm and Safe Multi-Objective Humanoid-dm environments.
  • Figure B.4: Safe Multi-Objective MuJoCo Environments. Specificaly, these environments are Safe Multi-Objective HalfCheetah (a), Safe Multi-Objective Hopper (b), Safe Multi-Objective Humanoid (c), Safe Multi-Objective Swimmer (d), Safe Multi-Objective Walker (e) and Safe Multi-Objective Pusher (f).
  • Figure B.5: More Experiments to evaluate the effectiveness of our method on Safe Multi-Objective MuJoCo environments regarding the reward and safety performance.

Theorems & Definitions (20)

  • Definition 3.1: Safe Pareto Frontier
  • Theorem 5.2
  • Lemma Appendix A.1: Multi-objective NPG
  • proof
  • Lemma Appendix A.2
  • proof
  • Lemma Appendix A.3
  • proof
  • Lemma Appendix A.4: dalal2018finite
  • Lemma Appendix A.5
  • ...and 10 more