  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.
