Partitioned Linear Programming Approximations for MDPs
This work addresses scalability issues in MDPs for AI and operations research, offering an incremental improvement over existing approximate linear programming methods.
The paper tackles the computational challenge of solving large factored Markov decision processes (MDPs) by proposing a partitioned linear programming approximation that decomposes constraint spaces into low-dimensional ones, enabling efficient solving and scaling to MDPs with over 2^100 states.
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize their weights by linear programming (LP). This paper proposes a new ALP approximation. Comparing to the standard ALP formulation, we decompose the constraint space into a set of low-dimensional spaces. This structure allows for solving the new LP efficiently. In particular, the constraints of the LP can be satisfied in a compact form without an exponential dependence on the treewidth of ALP constraints. We study both practical and theoretical aspects of the proposed approach. Moreover, we demonstrate its scale-up potential on an MDP with more than 2^100 states.