Convergence and Sample Complexity of Natural Policy Gradient Primal-Dual Methods for Constrained MDPs

2024-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new Natural Policy Gradient Primal-Dual (NPG-PD) method is proposed for solving discounted infinite-horizon optimal control problems in Constrained Markov Decision Processes (constrained MDPs). This method addresses sequential decision-making by maximizing expected total reward subject to an expected total utility constraint. The NPG-PD algorithm updates the primal variable using natural policy gradient ascent and the dual variable via projected subgradient descent. Despite the nonconcave objective and nonconvex constraint set, the method achieves global convergence with sublinear rates for both optimality gap and constraint violation under softmax policy parametrization. This convergence is dimension-free, meaning it is independent of the state-action space size. For log-linear and general smooth policy parametrizations, sublinear convergence rates are established, accounting for function approximation error. The paper also provides convergence and finite-sample complexity guarantees for two sample-based NPG-PD algorithms, validated through computational experiments.

Key takeaway

For research scientists developing reinforcement learning algorithms for constrained environments, the NPG-PD method offers a robust approach to achieving global convergence in constrained MDPs. You should consider implementing this method, particularly with softmax policy parametrization, to ensure dimension-free sublinear convergence rates. This could significantly improve the reliability and scalability of your constrained optimal control solutions, especially in complex, large-scale state-action spaces.

Key insights

The NPG-PD method globally converges sublinearly for constrained MDPs, independent of state-action space size.

Principles

• Primal-dual methods can solve nonconcave/nonconvex constrained MDPs.
• Natural policy gradient ascent updates primal variables effectively.
• Projected subgradient descent updates dual variables effectively.

Method

The NPG-PD method updates the primal variable via natural policy gradient ascent and the dual variable via projected subgradient descent to solve constrained MDPs.

In practice

• Apply NPG-PD to optimize reward under utility constraints.
• Use softmax parametrization for dimension-free convergence.
• Consider sample-based NPG-PD for practical implementations.

Topics

• Constrained MDPs
• Natural Policy Gradient
• Primal-Dual Methods
• Sample Complexity
• Policy Optimization

Best for: Research Scientist, AI Researcher, AI Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.