Point-wise maximum approach to approximate dynamic programming

Paul N. Beuchat, Joseph Warrington, John Lygeros

Abstract: In this paper we study value function approximation techniques that are based on the Linear Programming formulation of Approximate Dynamic Programming. We propose a point-wise maximum adaptation of the Linear Programming formulation, which renders the problem nonlinear and non-convex. We show that the proposed formulation is equivalent to the Linear Programming formulation, and we apply a series of approximation steps to develop an iterative algorithm for computing value function approximations. We demonstrate the computational advantages and approximation quality of the proposed algorithm through numerical examples on systems of low and high dimension.