On the dynamic stochastic approximation

Dynamic Stochastic Approximation for Multi-stage Stochastic Optimization

In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm, for solving these types of stochastic optimization problems. We show that DSA can achieve an optimal O(1/ǫ4) rate of convergence in terms of the total numbe...

On Stochastic Approximation

This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested. by Robbins and Monro [1]. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic mean).

On the approximation of stochastic integrals

Approximation Strategies for Routing in Stochastic Dynamic Networks

In this work, we study a special semi-Markov decision process that formalizes a route-planning problem in stochastic transportation networks. We explore two versions of the planning problem: one in which the planner knows the initial traffic situation but does not have access to further information once it begins executing the plan (open-loop), and one in which the planner receives continuous t...

Successive Linear Approximation Solution of Infinite-Horizon Dynamic Stochastic Programs

Models for long-term planning often lead to infinite horizon stochastic programs that offer significant challenges for computation. Finite-horizon approximations are often used in these cases but they may also become computationally difficult. In this paper, we directly solve for value functions of infinite horizon stochastic programs. We show that a successive linear approximation method conve...