Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems
Optimization and Control
2025-04-30 v2 Probability
Abstract
In this note we provide an upper bound for the difference between the value function of a distributionally robust Markov decision problem and the value function of a non-robust Markov decision problem, where the ambiguity set of probability kernels of the distributionally robust Markov decision process is described by a Wasserstein-ball around some reference kernel whereas the non-robust Markov decision process behaves according to a fixed probability kernel contained in the ambiguity set. Our derived upper bound for the difference between the value functions is dimension-free and depends linearly on the radius of the Wasserstein-ball.
Keywords
Cite
@article{arxiv.2308.05520,
title = {Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems},
author = {Ariel Neufeld and Julian Sester},
journal= {arXiv preprint arXiv:2308.05520},
year = {2025}
}