Abstract Imprecise-reward Markov decision processes (IRMDPs) are MDPs in which the reward function is only partially speci?ed (e.g., by some elicitation process). Recent work using minimax regret to solve IRMDPs has shown, despite their theoretical intractability, how the set of policies that are nondominated w.r.t. reward uncertainty can be exploited to accelerate regret computation. However, the number of nondominated policies is generally so large as to undermine this leverage. In this paper, we show how the quality of the approximation can be improved online by pruning/adding nondominated policies during reward elicitation, while maintaining computational tractability. Drawing insights from the POMDP literature, we also develop a new anytime algorithm for constructing the set of nondominated policies with provable (anytime) error bounds. These bounds can be exploited to great effect in our online approximation scheme.