A Geometric Traversal Algorithm for Reward-Uncertain MDPs

TL;DR

This paper introduces a geometric traversal algorithm for efficiently computing robust policies in reward-uncertain MDPs, significantly improving performance over previous methods.

Contribution

The paper presents a novel geometric traversal algorithm for reward-uncertain MDPs, enabling faster computation of minimax regret policies.

Findings

Algorithm improves performance by orders of magnitude

Efficiently computes the set of all potentially optimal policies

Includes an approximate version for faster computation

Abstract

Markov decision processes (MDPs) are widely used in modeling decision making problems in stochastic environments. However, precise specification of the reward functions in MDPs is often very difficult. Recent approaches have focused on computing an optimal policy based on the minimax regret criterion for obtaining a robust policy under uncertainty in the reward function. One of the core tasks in computing the minimax regret policy is to obtain the set of all policies that can be optimal for some candidate reward function. In this paper, we propose an efficient algorithm that exploits the geometric properties of the reward function associated with the policies. We also present an approximate version of the method for further speed up. We experimentally demonstrate that our algorithm improves the performance by orders of magnitude.