Quantitative Analysis of $ω$-Regular Robust MDPs· ω-正则鲁棒MDP的定量分析

Robust Markov Decision Processes (RMDPs) generalize classical MDPs by allowing uncertainty in transition probabilities and optimizing against their worst-case realization. We consider $(s,a)$-rectangular RMDPs with \emph{linearly defined} uncertainty sets and study parity objectives, which are a canonical representation of $ω$-regular objectives. An uncertainty set is linearly defined if it is described by linear inequalities over the transition distribution together with auxiliary variables, which capture the standard $L_1$ and $L_\infty$ balls as well as general polytopic uncertainty sets. The quantitative value is the supremum, over all agent policies, of the satisfaction probability guaranteed against the adversarial environment. Previous work studied the qualitative analysis, namely t