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We use the technique of information relaxation to develop a duality-driveniterative approach to obtaining and improving confidence interval estimates forthe true value of finite-horizon stochastic dynamic programming problems. Weshow that the sequence of dual value estimates yielded from the proposedapproach in principle monotonically converges to the true value function in afinite number of dual iterations. Aiming to overcome the curse ofdimensionality in various applications, we also introduce a regression-basedMonte Carlo algorithm for implementation. The new approach can be used not onlyto assess the quality of heuristic policies, but also to improve them if wefind that their duality gap is large. We obtain the convergence rate of ourMonte Carlo method in terms of the amounts of both basis functions and thesampled states. Finally, we demonstrate the effectiveness of our method in anoptimal order execution problem with market friction and in an inventorymanagement problem in the presence of lost sale and lead time. Both examplesare well known in the literature to be difficult to solve for optimality. Theexperiments show that our method can significantly improve the heuristicssuggested in the literature and obtain new policies with a satisfactoryperformance guarantee.

Information Relaxation and A Duality-Driven Algorithm for Stochastic Dynamic Programs