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We present an algorithm for formal verification and parameter synthesis ofcontinuous state-space Markov chains. This class of problems captures thedesign and analysis of a wide variety of autonomous and cyber-physical systemsdefined by nonlinear and black-box modules. In order to solve these problems,one has to maximize certain probabilistic objective functions overall choicesof initial states and parameters. In this paper, we identify the assumptionsthat make it possible to view this problem as a multi-armed bandit problem.Based on this fresh perspective, we propose an algorithm (HOO-MB) for solvingthe problem that carefully instantiates an existing bandit algorithm --Hierarchical Optimistic Optimization -- with appropriate parameters. As aconsequence, we obtain theoretical regret bounds on sample efficiency of oursolution that depends on key problem parameters like smoothness,near-optimality dimension, and batch size. The batch size parameter enables usto strike a balance between the sample efficiency and the memory usage of thealgorithm. Our experiments, using the tool HooVer, suggest that the approachscales to realistic-sized problems and is often more sample-efficient comparedto PlasmaLab -- a leading tool for verification of stochastic systems.Specifically, HooVer has distinct advantages in analyzing models in which theobjective function has sharp slopes. In addition, HooVer shows promisingbehavior in parameter synthesis for a linear quadratic regulator (LQR) example.

Verification and Parameter Synthesis for Stochastic Systems using Optimistic Optimization