Sound Heuristic Search Value Iteration for Undiscounted POMDPs with Reachability Objectives

TL;DR

This paper introduces a novel heuristic search value iteration algorithm for undiscounted POMDPs with reachability objectives, improving efficiency and policy quality by leveraging bounds and informed exploration.

Contribution

It extends point-based methods to indefinite-horizon reachability problems in POMDPs, providing a new algorithm with convergence guarantees and superior performance.

Findings

Outperforms existing methods in probability guarantees

Reduces computation time significantly

Provides policies with two-sided bounds on reachability probabilities

Abstract

Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the (indefinite-horizon) Maximal Reachability Probability Problem (MRPP), where the goal is to maximize the probability of reaching some target states. This is also a core problem in model checking with logical specifications and is naturally undiscounted (discount factor is one). Inspired by the success of point-based methods developed for discounted problems, we study their extensions to MRPP. Specifically, we focus on trial-based heuristic search value iteration techniques and present a novel algorithm that leverages the strengths of these techniques for efficient exploration of the belief space (informed search via value bounds) while addressing their drawbacks in handling loops for indefinite-horizon problems. The algorithm produces policies with two-sided bounds on optimal reachability probabilities. We prove convergence to an optimal policy from below under certain conditions. Experimental evaluations on a suite of benchmarks show that our algorithm outperforms existing methods in almost all cases in both probability guarantees and computation time.