Policy Gradient for Continuous-Time Robust Markov Decision Processes

arXiv:2606.04335v1 Announce Type: new 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 $\tilde{\mathcal{O}}(\frac{1}{\epsilon^2})$ 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 $\tilde{\mathcal{O}}(\frac{N^2}{\epsilon})$ 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.

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 $\tilde{\mathcal{O}}(\frac{1}{\epsilon^2})$ 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 $\tilde{\mathcal{O}}(\frac{N^2}{\epsilon})$ 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.

Machine Learning (cs.LG); Systems and Control (eess.SY)

arXiv:2606.04335 [cs.LG]

(or arXiv:2606.04335v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.04335 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Policy Gradient for Continuous-Time Robust Markov Decision Processes

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