Lina Gerlach

Lina Gerlach, Tobias Winkler, Erika Ábrahám et al.

Probabilistic hyperproperties describe probabilistic relations between multiple sets of executions in a stochastic system. Prominent examples include information-theoretic characterizations of security and privacy policies. However, model checking for existing probabilistic hyperlogics, such as HyperPCTL and PHL, is undecidable in Markov decision processes (MDPs). In this paper, we study an underexplored problem: the verification of fragments of probabilistic hyperproperties that relate the probabilities of different events to each other, possibly across independent executions of an MDP. Representative verification questions include: Can two different target states be reached from the same initial state with the same probability? (different events), Can a given target state be reached from two different initial states with the same probability? (same event, independent executions), and natural combinations of these forms. Besides reachability, our relational probabilistic properties cover safety, Büchi, and coBüchi objectives. They can also be combined conjunctively, thereby generalizing standard multi-objective MDP properties. We provide efficient algorithms for relevant classes of relational properties, while proving computational hardness and completeness results for others. An implementation of our approach outperforms solvers for more general probabilistic hyperlogics by orders of magnitude on the subset of their benchmarks that lies within our fragment.

Paul Kobialka, Lina Gerlach, Francesco Leofante et al.

Counterfactuals are widely used in AI to explain how minimal changes to a model's input can lead to a different output. However, established methods for computing counterfactuals typically focus on one-step decision-making, and are not directly applicable to sequential decision-making tasks. This paper fills this gap by introducing counterfactual strategies for Markov Decision Processes (MDPs). During MDP execution, a strategy decides which of the enabled actions (with known probabilistic effects) to execute next. Given an initial strategy that reaches an undesired outcome with a probability above some limit, we identify minimal changes to the initial strategy to reduce that probability below the limit. We encode such counterfactual strategies as solutions to non-linear optimization problems, and further extend our encoding to synthesize diverse counterfactual strategies. We evaluate our approach on four real-world datasets and demonstrate its practical viability in sophisticated sequential decision-making tasks.