Heuristic Search in Dual Space for Constrained Fixed-Horizon POMDPs with Durative Actions.

The Partially Observable Markov Decision Process (POMDP) is widely used in probabilistic planning for stochastic domains. However, current extensions, such as constrained and chance-constrained POMDPs, have limitations in modeling real-world planning problems because they assume that all actions have a fixed duration. To address this issue, we propose a unified model that encompasses durative POMDP and its constrained extensions. To solve the durative POMDP and its constrained extensions, we first convert them into an Integer Linear Programming (ILP) formulation. This approach leverages existing solvers in the ILP literature and provides a foundation for solving these problems. We then introduce a heuristic search approach that prunes the search space, which is guided by solving successive partial ILP programs. Our empirical evaluation results show that our approach outperforms the current state-of-the-art fixed-horizon chance-constrained POMDP solver.