On the convergence of stochastic dual dynamic programming and related methods

We discuss the almost-sure convergence of a broad class of sampling algorithms for multi-stage stochastic linear programs. We provide a convergence proof based on the finiteness of the set of distinct cutcoefficients. This differs from existing published proofs in that it does not require a restrictive assumption

Regularized Decomposition of High-Dimensional Multistage Stochastic Programs with Markov Uncertainty

We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource state variable, and a Markov information process. The resulting algorithms are shown to converge to an optimal policy after a finite number of iterations under mild technical assumptions. Computational experiments are conducted using the setting of optimizing energy storage over a large transmission grid, which motivates both the spatial and temporal dimensions of our problem. Our numerical results indicate that the proposed methods exhibit significantly faster convergence than their classical counterparts, with greater gains observed for higher-dimensional problems