Wasserstein-robust finite-horizon MDP values admit exact directional-derivative policy-gradient recursions, reducing to a vector-valued gradient when the dual and transport optimizers are unique.
Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs
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abstract
We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context of optimal control and optimal stopping problems. Motivated by issues of sensitivity analysis in distributionally robust optimization (DRO) control and optimal stopping problems, we establish explicit formulas for the corresponding sensitivities under drift reference measure uncertainty. Our work is closely related to \citeauthor{bartl2023sensitivity} \cite{bartl2023sensitivity}. In contrast to the existing literature, our analysis is carried out within a general non-Markovian framework.
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Policy Gradient Learning for Distributionally Robust Markov Decision Processes under Wasserstein Ambiguity
Wasserstein-robust finite-horizon MDP values admit exact directional-derivative policy-gradient recursions, reducing to a vector-valued gradient when the dual and transport optimizers are unique.