A framework for parallel second order incremental optimization algorithms for solving partially separable problems

Kamer Kaya (), Figen Öztoprak (), Ş. İlker Birbil (), A. Taylan Cemgil (), Umut Şimşekli (), Nurdan Kuru (), Hazal Koptagel () and M. Kaan Öztürk ()
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Kamer Kaya: Sabanci University
Figen Öztoprak: Istanbul Bilgi University
Ş. İlker Birbil: Erasmus University Rotterdam
A. Taylan Cemgil: Boğaziçi University
Umut Şimşekli: Université Paris-Saclay
Nurdan Kuru: Sabanci University
Hazal Koptagel: Boğaziçi University
M. Kaan Öztürk: Sabanci University

Computational Optimization and Applications, 2019, vol. 72, issue 3, No 6, 675-705

Abstract: Abstract We propose Hessian Approximated Multiple Subsets Iteration (HAMSI), which is a generic second order incremental algorithm for solving large-scale partially separable convex and nonconvex optimization problems. The algorithm is based on a local quadratic approximation, and hence, allows incorporating curvature information to speed-up the convergence. HAMSI is inherently parallel and it scales nicely with the number of processors. We prove the convergence properties of our algorithm when the subset selection step is deterministic. Combined with techniques for effectively utilizing modern parallel computer architectures, we illustrate that a particular implementation of the proposed method based on L-BFGS updates converges more rapidly than a parallel gradient descent when both methods are used to solve large-scale matrix factorization problems. This performance gain comes only at the expense of using memory that scales linearly with the total size of the optimization variables. We conclude that HAMSI may be considered as a viable alternative in many large scale problems, where first order methods based on variants of gradient descent are applicable.

Keywords: Large-scale unconstrained optimization; Second order information; Shared-memory parallel implementation; Balanced coloring; Balanced stratification; Matrix factorization (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10589-018-00057-7

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