Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods-distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach turns ADP into an optimization problem, for which we derive new mathematical program formulations and analyze its properties. DRADP improves on the theoretical guarantees of existing ADP methods-it guarantees convergence and L 1 norm-based error bounds. The empirical evaluation of DRADP shows that the theoretical guarantees translate well into good performance on benchmark problems. Copyright 2012 by the author(s)/owner(s).