A Geometric Traversal Algorithm for Reward-Uncertain MDPs
This addresses the challenge of robust decision-making in stochastic environments for applications like robotics or finance, though it is incremental as it builds on existing minimax regret approaches.
The paper tackles the problem of computing robust policies in Markov decision processes with uncertain reward functions by proposing an efficient geometric traversal algorithm, which experimentally improves performance by orders of magnitude.
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.