Date of Original Version
Proceedings of the Twentieth International Conference on Machine Learning (ICML-2003), Washington DC, 2003
Abstract or Table of Contents
We investigate methods for planning in a Markov Decision Process where the cost function is chosen by an adversary after we x our policy. As a running example, we consider a robot path planning problem where costs are influenced by sensors that an adversary places in the environment. We formulate the problem as a zero-sum matrix game where rows correspond to deterministic policies for the planning player and columns correspond to cost vectors the adversary can select. For a fixed cost vector, fast algorithms (such as value iteration) are available for solving MDPs. We develop efficient algorithms for matrix games where such best response oracles exist. We show that for our path planning problem these algorithms are at least an order of magnitude faster than direct solution of the linear programming formulation.