Subsampling Algorithms for Semidefinite Programming

TL;DR

This paper introduces a stochastic gradient algorithm for semidefinite programming that employs subsampling to balance computational efficiency and solution complexity, demonstrating effectiveness on large-scale statistical learning problems.

Contribution

It presents a novel subsampling-based stochastic gradient method for semidefinite optimization with explicit control over computational tradeoffs and solution complexity.

Findings

Reduces per-iteration computational cost via subsampling.

Total cost scales with the solution's rank.

Effective on large-scale statistical learning problems.

Abstract

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls granularity, i.e. the tradeoff between cost per iteration and total number of iterations. Furthermore, the total computational cost is directly proportional to the complexity (i.e. rank) of the solution. We study numerical performance on some large-scale problems arising in statistical learning.