On Anderson acceleration for partially observable Markov decision processes

TL;DR

This paper introduces an accelerated offline solution method for POMDPs that combines Anderson acceleration with the fast informed bound, improving convergence speed while maintaining solution quality.

Contribution

It presents a novel combination of Anderson acceleration and FIB for POMDPs, with proven convergence and explicit error bounds, enhancing scalability and efficiency.

Findings

Faster convergence compared to standard methods

Maintains solution quality despite acceleration

Explicit error bounds for approximation

Abstract

This paper proposes an accelerated method for approximately solving partially observable Markov decision process (POMDP) problems offline. Our method carefully combines two existing tools: Anderson acceleration (AA) and the fast informed bound (FIB) method. Adopting AA, our method rapidly solves an approximate Bellman equation with an efficient combination of previous solution estimates. Furthermore, the use of FIB alleviates the scalability issue inherent in POMDPs. We show the convergence of the overall algorithm to the suboptimal solution obtained by FIB. We further consider a simulation-based method and prove that the approximation error is bounded explicitly. The performance of our algorithm is evaluated on several benchmark problems. The results of our experiments demonstrate that the proposed algorithm converges significantly faster without degrading the quality of the solution compared to its standard counterpart.