Title: Target Drift in Multi-Constraint Lagrangian RL: Theory and Practice
Primary area: reinforcement learning
Keywords: Energy System Operation, Safe, RL

Abstract: Lagrangian-based methods are one of the dominant approaches for safe reinforcement learning (RL) in constrained Markov decision processes, commonly used across domains with multiple constraints. While some implementations combine all constraints into a mixed penalty term and others use one estimator per constraint, the fundamental question of which design is theoretically sound has received little scrutiny. We provide the first theoretical analysis showing that the mixed-critic architecture induces a persistent bias due to target drift from evolving Lagrange multipliers. In contrast, dedicated-critic design—separate critics for reward and each constraint—avoids this issue. We also validate our findings in a simulated but realistic energy system with multiple physical constraints, where the dedicated-critic method achieves stable learning and consistent constraint satisfaction, while the mixed-critic method fails. Our results offer a principled argument for preferring dedicated-critic architectures in multi-constraint safe RL problems.