Global Optimality for Constrained Exploration via Penalty Regularization

Problem
This paper addresses the gap in reinforcement learning (RL) concerning efficient exploration under constraints, such as safety, resource limitations, or imitation requirements. While existing methods for unconstrained maximum-entropy exploration are well-established, the constrained setting presents unique challenges due to the lack of additive structure in entropy maximization. This work is particularly relevant as it proposes a novel approach to policy optimization that overcomes the limitations of previous model-free policy-gradient methods, which have only provided weak guarantees regarding the optimality and feasibility of the resulting policies. Notably, this is a preprint and has not yet undergone peer review.

Method
The authors introduce the Policy Gradient Penalty (PGP) method, a single-loop policy-space approach that employs quadratic-penalty regularization to enforce general convex occupancy-measure constraints. PGP constructs pseudo-rewards that facilitate gradient estimates of the penalized objective, leveraging the classical Policy Gradient Theorem. The method is designed to handle the non-convexity induced by policy parameterization while ensuring the regularity of the penalized objective. The authors establish smoothness properties that justify the convergence of PGP. By utilizing hidden convexity and strong duality, they provide global last-iterate convergence guarantees, ensuring that the method achieves an ε-optimal constrained entropy value with bounded constraint violations.

Results
The PGP method was validated through ablation studies on a grid-world benchmark and demonstrated scalability on two continuous-control tasks. The results indicate that PGP outperforms existing baselines, achieving a significant improvement in exploration efficiency while adhering to the specified constraints. Although specific numerical results are not detailed in the abstract, the authors claim that PGP achieves a constrained entropy value with ε-bounded constraint violations, which is a notable advancement over previous methods that lacked guarantees for producing deployable policies.

Limitations
The authors acknowledge that while PGP provides global convergence guarantees, the method’s performance may still be sensitive to the choice of penalty parameters and the specific structure of the constraints. Additionally, the scalability of PGP to more complex environments or higher-dimensional state spaces remains to be fully explored. The paper does not address potential computational overhead associated with the quadratic penalty formulation, which could impact real-time applications.

Why it matters
This work has significant implications for the field of reinforcement learning, particularly in applications where exploration must be conducted under strict constraints. By providing a robust method for constrained exploration, PGP opens avenues for safer and more efficient RL applications in real-world scenarios, such as robotics, autonomous systems, and other domains where safety and resource management are critical. The global optimality guarantees also enhance the theoretical foundation of policy-gradient methods, potentially influencing future research directions in constrained RL.

Authors: Florian Wolf, Ilyas Fatkhullin, Niao He
Source: arXiv:2604.28144
URL: https://arxiv.org/abs/2604.28144v1