INEXACT CUTS IN STOCHASTIC DUAL DYNAMIC PROGRAMMING

We introduce an extension of stochastic dual dynamic programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of the method are solved with bounded errors (inexactly). This inexact variant of SDDP is described for both linear problems (the corresponding variant being denoted by ISDDP-LP) and nonlinear problems (the corresponding variant being denoted by ISDDP-NLP). We prove convergence theorems for ISDDP-LP and ISDDP-NLP for both bounded and asymptotically vanishing errors. Finally, we present the results of numerical experiments comparing SDDP and ISDDP-LP on a portfolio problem with direct transaction costs modeled as a multistage stochastic linear optimization problem. In these experiments, ISDDP-LP allows us to strike a different balance between policy quality and computing time, trading off the former for the latter.