SONIA: A Symmetric Blockwise Truncated Optimization Algorithm

TL;DR

SONIA is a novel optimization algorithm that combines first- and second-order methods, effectively handling large-scale machine learning problems with theoretical convergence guarantees and demonstrated empirical performance.

Contribution

The paper introduces SONIA, a new symmetric blockwise truncated optimization algorithm that integrates partial curvature information for improved convergence in large-scale settings.

Findings

Converges to stationary points in convex and nonconvex cases.

Effective on standard machine learning benchmarks.

Includes a stochastic variant with theoretical guarantees.

Abstract

This work presents a new algorithm for empirical risk minimization. The algorithm bridges the gap between first- and second-order methods by computing a search direction that uses a second-order-type update in one subspace, coupled with a scaled steepest descent step in the orthogonal complement. To this end, partial curvature information is incorporated to help with ill-conditioning, while simultaneously allowing the algorithm to scale to the large problem dimensions often encountered in machine learning applications. Theoretical results are presented to confirm that the algorithm converges to a stationary point in both the strongly convex and nonconvex cases. A stochastic variant of the algorithm is also presented, along with corresponding theoretical guarantees. Numerical results confirm the strengths of the new approach on standard machine learning problems.