Online First-Order Framework for Robust Convex Optimization

Abstract

Robust optimization (RO) is a technique to tractably model uncertain parameters in optimization problems. More recently, it has attracted interest in applications from machine learning and statistics. These recent applications present algorithmic challenges in which the scalability of RO algorithms with problem dimension becomes crucial. The traditional solution method for RO is to transform it into an equivalent—yet more complex—deterministic problem. The alternate solution technique is to iteratively solve sequences of the underlying deterministic model with different values of the uncertain parameters. However, such iterative approaches have been rather prohibitive in practice, especially when solving even the underlying deterministic model is expensive. In “Online First-Order Framework for Robust Convex Optimization,” by analyzing the structure of an underlying convex–nonconcave saddle point problem, N. Ho-Nguyen and F. Kılınç-Karzan develop an iterative framework for RO in which the cost of each iteration can be remarkably reduced. In particular, they show that, without scarifying from the guarantees on the number of iterations needed, it is possible to use cheap first-order updates instead of deterministic optimization solvers in each iteration.