Policy Gradient for Continuous-Time Robust Markov Decision Processes

• URL: http://arxiv.org/abs/2606.04335v2
• Date: Thu, 04 Jun 2026 10:50:34 GMT
• Title: Policy Gradient for Continuous-Time Robust Markov Decision Processes
• Abstract summary: This paper investigates policy algorithms within a continuous-time Markov decision processes framework.<n>Policy gradients and adversarial gradients are derived using pathwise and adjoint-based formulas.<n>We propose mean-field optimisers as distributional optimisers with an $tildemathcalO(frac1K)$ oracle-based convergence rate and an $tildemathcalO(fracN2)$ sample complexity under $N$-particle approximation.
• Score: 11.595126166975854
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The framework of robust Markov decision processes (RMDPs) allows the design of reinforcement learning agents that satisfy performance guarantees under worst-case transition dynamics. Traditional RMDPs consider discrete-time dynamics and recently, sample-efficient policy gradient algorithms have been considered in this context. This paper investigates policy gradient algorithms within a continuous-time RMDP framework. Policy gradients and adversarial gradients are derived using pathwise and adjoint-based formulas for stochastic and ordinary differential equations. We propose double-loop optimisers to obtain linear convergence in the oracle-based setting and an $\tilde{\mathcal{O}}(\frac{1}{ε^2})$ sample complexity in the sample-based setting in an analysis which also derives novel tools for the framework of undiscounted total cost MDPs. Additionally, we propose mean-field optimisers as distributional optimisers with an $\tilde{\mathcal{O}}(\frac{1}{K})$ oracle-based convergence rate and an $\tilde{\mathcal{O}}(\frac{N^2}ε)$ sample complexity under $N$-particle approximation. The effectiveness of continuous-time policy gradient algorithms is confirmed for both optimisers on continuous-time RMDPs with neural ordinary differential equation dynamics.

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