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Subsampling algorithms for semidefinite programming

Author(s): Alexandre W. d'Aspremont

Journal: Stochastic Systems
ISSN 1946-5238

Volume: 1;
Issue: 2;
Start page: 274;
Date: 2011;
Original page

Keywords: Semidefinite programming | stochastic optimization | subsampling

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.

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