Safe Multi-Objective Reinforcement Learning: Zero Constraint Violation and Primal-Averaging Convergence
Authors: Chenxi Li, Yao Shu, Siyang Gao, Shuang Qiu, Guangxin Jiang
Organizations: Harbin Institute of Technology, Harbin, Heilongjiang, China · The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong, China · City University of Hong Kong, Hong Kong, China
Many applications of multi-objective reinforcement learning (MORL) require policies that balance conflicting objectives while satisfying safety constraints. We study safe MORL with zero constraint violation throughout learning, covering both cumulative and stepwise constraints. A key challenge is to explore sufficiently under unknown dynamics and constraint costs without violating the constraints. For a given preference over objectives, we develop an algorithm to learn a safe Pareto optimal policy by combining optimistic reward estimates with pessimistic cost bounds. With high probability, every policy executed over T episodes incurs zero constraint violation. The algorithm returns a safe Markov policy induced by the averaged occupancy measure and achieves an O(1/T) suboptimality gap under smooth Tchebycheff scalarization. We further develop a preference-free algorithm that first explores safely without a prespecified preference and then computes a safe policy for any given preference without further interaction. Over T exploration episodes and K planning iterations, it retains the same safety guarantee and achieves an O(1/T+1/K) suboptimality gap. Both algorithms require knowledge of a policy that strictly satisfies the constraints and its costs. We then relax these requirements, incurring at most constant cumulative violation. To our knowledge, we provide the first sample-efficient MORL algorithms that guarantee safety for every executed policy.
In safety-critical domains, reinforcement learning (RL) systems must satisfy strict, zero-cost safety constraints while achieving meaningful task performance. Existing model-free methods can struggle to achieve high safety without substantially compromising task performance. We introduce Safety-Biased Trust Region Policy Optimisation (SB-TRPO), a principled approach to RL with zero-cost constraints, which requires only a fixed fraction of the maximal cost reduction achievable within the trust region, thus retaining flexibility for reward optimisation. We show that the idealised update nevertheless converges to zero cost and maximal reward amongst zero-cost policies in finite MDPs. A practical gradient-based approximation provides local improvements in both safety and reward under suitable gradient alignment. Experiments on Safety Gymnasium demonstrate high safety alongside strong task performance.
Multi-Objective Reinforcement Learning (MORL) extends standard RL by optimizing policies with respect to multiple, often conflicting, objectives. While max-min MORL has emerged as an effective approach for promoting fairness, its applicability remains limited, particularly when constraints must be incorporated. In this paper, we propose a MORL framework that integrates the max-min criterion with explicit constraint satisfaction. We establish a theoretical foundation for the proposed framework and validate the resulting algorithm through convergence analysis and experiments in tabular settings. We further demonstrate the practical relevance of our approach in simulated building thermal control, multi-objective locomotion control, and greenhouse-gas-emission-aware traffic management. Across these domains, our method effectively balances fairness and constraint satisfaction in multi-objective decision-making.
Giseung Park, Hyunyoung Nam, Woohyeon Byeon +2
Robotics Institute, University of Toronto, 55 St George St, Toronto, Canada. · School of Electical Engineering, KAIST, Daejeon 34141, Republic of Korea. · Faculty of Engineering, Bar-Ilan University, Ramat Gan 52900, Israel.
Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose Constraint-Sensitive Policy Optimization (CSPO), a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods