Montenegro, A., Mussi, M., Papini, M., & Metelli, A. M. (2024). Last-Iterate Global Convergence of Policy Gradients for Constrained Reinforcement Learning. In Proceedings of the 38th Conference on Neural Information Processing Systems (NeurIPS 2024).
This paper aims to develop a policy gradient framework for constrained reinforcement learning (CRL) that provides global last-iterate convergence guarantees while being applicable to both action-based and parameter-based exploration paradigms. The authors address the limitations of existing methods, which often struggle with scalability to continuous control problems, limited policy parameterizations, and handling multiple constraints.
The authors propose a novel algorithm called C-PG, which utilizes a primal-dual optimization approach with a regularized Lagrangian function. They analyze the convergence properties of C-PG under weak gradient domination assumptions and demonstrate its effectiveness in handling continuous state and action spaces, multiple constraints, and different risk measures. Furthermore, they introduce two specific versions of C-PG: C-PGAE for action-based exploration and C-PGPE for parameter-based exploration.
The paper theoretically proves that C-PG achieves global last-iterate convergence to an optimal feasible policy, exhibiting dimension-free convergence rates independent of the state and action space sizes. Empirical evaluations on benchmark constrained control problems, including a Discrete Grid World with Walls and a CostLQR, demonstrate that C-PGAE and C-PGPE outperform state-of-the-art baselines like NPG-PD and RPG-PD in terms of sample efficiency.
The C-PG framework offers a robust and efficient solution for tackling constrained continuous control problems in reinforcement learning. Its theoretical guarantees and empirical performance suggest its potential for real-world applications requiring constraint satisfaction, such as robotics and autonomous systems.
This research significantly contributes to the field of constrained reinforcement learning by introducing a theoretically sound and practically effective policy gradient framework. The proposed C-PG algorithm, with its global convergence guarantees and flexibility in handling different exploration paradigms and risk measures, paves the way for developing more reliable and efficient CRL algorithms for complex control tasks.
While the paper provides a comprehensive analysis of C-PG, it acknowledges that further investigation is needed to extend the convergence guarantees to risk-based objectives beyond expected costs. Exploring the application of C-PG to more challenging real-world scenarios and investigating its compatibility with different policy parameterizations and risk measures are promising avenues for future research.
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by Alessandro M... at arxiv.org 11-13-2024
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