Commentary—Perspectives on Stochastic Optimization Over Time

Assortment optimization over time

In this note we introduce the problem of assortment optimization over time. We have a sequence of time steps and can introduce one new product per time step. Once introduced a product can not be removed. The goal is to determine which products to introduce so as to maximize revenue over all time steps under some choice model. Given a 1/α-approximation algorithm for the capacitated assortment op...

Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem

We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic MultiObjective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation method (SAA-N, where N is t...

Optimizing Space-time Codes via Stochastic Optimization

Linear dispersion (LD) codes are a good candidate for high data rate MIMO signaling. Traditionally LD codes were designed by maximizing the average mutual information, which cannot guarantee good error performance. This paper presents a design scheme for LD codes that directly minimizes bit/block error probability in (possibly spatially correlated) fading MIMO channels with an arbitrary receive...

Second Order Stochastic Optimization in Linear Time

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we develop second-order stochastic methods for optimization problems in machine ...

Optimization of Discrete-time, Stochastic Systems