Solving Constrained Stochastic Shortest Path Problems with Scalarisation

Constrained Stochastic Shortest Path Problems (CSSPs) model problems with probabilistic effects, where a primary cost is minimised subject to constraints over secondary costs, e.g., minimise time subject to monetary budget. Current heuristic search algorithms for CSSPs solve a sequence of increasingly larger CSSPs as linear programs until an optimal solution for the original CSSP is found. In this paper, we introduce a novel algorithm CARL, which solves a series of unconstrained Stochastic Shortest Path Problems (SSPs) with efficient heuristic search algorithms. These SSP subproblems are constructed with scalarisations that project the CSSP's vector of primary and secondary costs onto a scalar cost. CARL finds a maximising scalarisation using an optimisation algorithm similar to the subgradient method which, together with the solution to its associated SSP, yields a set of policies that are combined into an optimal policy for the CSSP. Our experiments show that CARL solves 50% more problems than the state-of-the-art on existing benchmarks.

Efficient Constraint Generation for Stochastic Shortest Path Problems

Current methods for solving Stochastic Shortest Path Problems (SSPs) find states' costs-to-go by applying Bellman backups, where state-of-the-art methods employ heuristics to select states to back up and prune. A fundamental limitation of these algorithms is their need to compute the cost-to-go for every applicable action during each state backup, leading to unnecessary computation for actions identified as sub-optimal. We present new connections between planning and operations research and, using this framework, we address this issue of unnecessary computation by introducing an efficient version of constraint generation for SSPs. This technique allows algorithms to ignore sub-optimal actions and avoid computing their costs-to-go. We also apply our novel technique to iLAO* resulting in a new algorithm, CG-iLAO*. Our experiments show that CG-iLAO* ignores up to 57% of iLAO*'s actions and it solves problems up to 8x and 3x faster than LRTDP and iLAO*.