Future AGIs will need to solve large reinforcement-learning problems involving complex reward functions having multiple reward sources. One way to make progress on such problems is to decompose them into smaller regions that can be solved efficiently. We introduce a novel modular version of Least Squares Policy Iteration (LSPI), called M-LSPI, which 1. breaks up Markov decision problems (MDPs) into a set of mutually exclusive regions; 2. iteratively solves each region by a single matrix inversion and then combines the solutions by value iteration. The resulting algorithm leverages regional decomposition to efficiently solve the MDP. As the number of states increases, on both structured and unstructured MDPs, M-LSPI yields substantial improvements over traditional algorithms in terms of time to convergence to the value function of the optimal policy, especially as the discount factor approaches one.