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arXiv · 2610.31094

Policy Evaluation and Policy Gradient for Continuous-Time Markov Regime-Switching Systems

Minghui Zhang·Xun Li·Xin Zhang
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Abstract

We study policy evaluation (PE) and policy gradient (PG) for continuous-time stochastic control with Markov regime-switching. The main challenges are the coexistence of diffusion and regime jumps, the coupling of regime-dependent value functions, and the construction of model-free learning rules from the coupled generators. We establish a martingale characterization of PE that incorporates both Brownian and switching martingales, and extend martingale loss and orthogonality methods to this setting. We further derive a coupled PG equation and a trajectory-based gradient representation that, under an action-independent switching generator, avoids explicit knowledge of the system coefficients and transition rates. These results lead to offline and online actor-critic algorithms. We also establish convergence and study the finite-grid approximation required for implementation. Numerical experiments for a regime-switching linear-quadratic problem illustrate the proposed methods.

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Minghui Zhang, Xun Li, Xin Zhang. 2026-10-22. Policy Evaluation and Policy Gradient for Continuous-Time Markov Regime-Switching Systems. https://arxiv.org/abs/2610.31094

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