Pratyush Agarwal | Searcharxiv

arXiv2023

Upper Bounds for All and Max-gain Policy Iteration Algorithms on Deterministic MDPs

Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs (DMDPs): the class of MDPs in which every state-action pair has a unique next state. Our results include a non-trivial upper bound that applies to the entire family of PI algorithms; another to all "max-gain" switching variants; and affirmation that a conjecture regarding Howard's PI on MDPs is true for DMDPs. Our analysis is based on certain graph-theoretic results, which may be of independent interest.

cs.DM↗

arXiv2021

Stateless Model Checking under a Reads-Value-From Equivalence

Stateless model checking (SMC) is one of the standard approaches to the verification of concurrent programs. As scheduling non-determinism creates exponentially large spaces of thread interleavings, SMC attempts to partition this space into equivalence classes and explore only a few representatives from each class. The efficiency of this approach depends on two factors: (a) the coarseness of the partitioning, and (b) the time to generate representatives in each class. For this reason, the search for coarse partitionings that are efficiently explorable is an active research challenge. In this work we present RVF-SMC, a new SMC algorithm that uses a novel \emph{reads-value-from (RVF)} partitioning. Intuitively, two interleavings are deemed equivalent if they agree on the value obtained in each read event, and read events induce consistent causal orderings between them. The RVF partitioning is provably coarser than recent approaches based on Mazurkiewicz and "reads-from" partitionings. Our experimental evaluation reveals that RVF is quite often a very effective equivalence, as the underlying partitioning is exponentially coarser than other approaches. Moreover, RVF-SMC generates representatives very efficiently, as the reduction in the partitioning is often met with significant speed-ups in the model checking task.

cs.PL↗