Robust Verification of Concurrent Stochastic Games
Angel Y. He, David Parker
TL;DR
This work tackles the verification of concurrent stochastic games under transition-uncertainty by introducing robust CSGs (RCSGs) and their interval subclass ICSGs. It develops a principled, worst-case verification framework that reduces robustness to standard CSG techniques via adversarial expansions, handling both finite/infinite horizons and zero-sum and nonzero-sum objectives. The authors define robust equilibria (RNE, RSWNE), prove key properties such as value equivalence and memoryless optimality, and provide concrete algorithms (RVI/RBI) plus inner optimization procedures, with and without explicit construction of expanded games. Implemented in PRISM-games and evaluated on large benchmarks, the approach shows zero-sum ICSGs scale comparably to non-robust CSGs, while nonzero-sum ICSGs remain tractable for sizable models, highlighting the practicality of robust multi-agent verification under transition uncertainty.
Abstract
Autonomous systems often operate in multi-agent settings and need to make concurrent, strategic decisions, typically in uncertain environments. Verification and control problems for these systems can be tackled with concurrent stochastic games (CSGs), but this model requires transition probabilities to be precisely specified - an unrealistic requirement in many real-world settings. We introduce *robust CSGs* and their subclass *interval CSGs* (ICSGs), which capture epistemic uncertainty about transition probabilities in CSGs. We propose a novel framework for *robust* verification of these models under worst-case assumptions about transition uncertainty. Specifically, we develop the underlying theoretical foundations and efficient algorithms, for finite- and infinite-horizon objectives in both zero-sum and nonzero-sum settings, the latter based on (social-welfare optimal) Nash equilibria. We build an implementation in the PRISM-games model checker and demonstrate the feasibility of robust verification of ICSGs across a selection of large benchmarks.