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Approximate linear programming (ALP) is an efficient approach to solvinglarge factored Markov decision processes (MDPs). The main idea of the method isto approximate the optimal value function by a set of basis functions andoptimize their weights by linear programming (LP). This paper proposes a newALP approximation. Comparing to the standard ALP formulation, we decompose theconstraint space into a set of low-dimensional spaces. This structure allowsfor solving the new LP efficiently. In particular, the constraints of the LPcan be satisfied in a compact form without an exponential dependence on thetreewidth of ALP constraints. We study both practical and theoretical aspectsof the proposed approach. Moreover, we demonstrate its scale-up potential on anMDP with more than 2^100 states.

Partitioned Linear Programming Approximations for MDPs