A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity computing optimal solutions characterized by Bellman's principle optimality. A wide range approximate (ADP) now exists. It is great to guarantee that performance an ADP scheme be at least some known fraction, say ?, optimal. This letter introduces a general approach bounding methods, this sense, stochastic setting. The based on new results greedy string optimization where one choose (ordered set) actions maximize objective function. technique inspired submodularity theory, but not required establishing bounds. Instead, quantifying certain notions curvature functions; smaller curvatures better bound. key insight any surrogate function coincides its solution and value with those original control problem. then yields mentioned above, determine ? depend specific ADP.