Mitigation of Curse of Dimensionality in Dynamic Programming

Abstract

Abstract Dynamic programming, one of the most powerful solution methodologies to achieve optimality for separable optimization problems, suffers heavily from the notorious “curse of dimensionality”, which prevents its direct applications when the dimension of the state space is high. By aggregating multiple constraints into a single surrogate constraint, the surrogate constraint formulation offers an ideal platform for powerful utilization of dynamic programming, although often with a price of a presence of duality gap. In this paper, we propose a novel convergent dynamic programming algorithm by integrating a domain cut scheme with the surrogate constraint formulation, thus enabling elimination of the duality gap gradually in the solution process.