SONIA: A Symmetric Blockwise Truncated Optimization Algorithm

• URL: http://arxiv.org/abs/2006.03949v1
• Date: Sat, 6 Jun 2020 19:28:14 GMT
• Title: SONIA: A Symmetric Blockwise Truncated Optimization Algorithm
• Authors: Majid Jahani, Mohammadreza Nazari, Rachael Tappenden, Albert S. Berahas, Martin Tak\'a\v{c}
• Abstract summary: This work presents a new algorithm for empirical risk. The algorithm bridges the gap between first- and second-order search methods by computing a second-order search-type update in one subspace, coupled with a scaled steepest descent step in the Theoretical complement.
• Score: 2.9923891863939938
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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