Online POMDP Planning with Anytime Deterministic Optimality Guarantees

TL;DR

This paper introduces a method to provide deterministic optimality guarantees for online POMDP solvers, enabling certification of solution quality and potentially improving decision-making performance under uncertainty.

Contribution

The authors derive a deterministic relationship between approximate and optimal solutions in POMDPs, enabling bounds and guarantees with minimal computational overhead.

Findings

Derived bounds relate approximate solutions to the optimal in POMDPs

Guarantees can be integrated into existing algorithms with little overhead

Deterministic certification can lead to better decision performance

Abstract

Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating decision-making problems under such conditions. However, finding an optimal solution for a POMDP is generally intractable. In recent years, there has been a significant progress of scaling approximate solvers from small to moderately sized problems, using online tree search solvers. Often, such approximate solvers are limited to probabilistic or asymptotic guarantees towards the optimal solution. In this paper, we derive a deterministic relationship for discrete POMDPs between an approximated and the optimal solution. We show that at any time, we can derive bounds that relate between the existing solution and the optimal one. We show that our derivations provide an avenue for a new set of algorithms and can be attached to existing algorithms that have a certain structure to provide them with deterministic guarantees with marginal computational overhead. In return, not only do we certify the solution quality, but we demonstrate that making a decision based on the deterministic guarantee may result in superior performance compared to the original algorithm without the deterministic certification.