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arXiv · 1206.4627

Convergence Rates of Biased Stochastic Optimization for Learning Sparse Ising Models

Jean Honorio
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Abstract

We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising models. We first provide a convergence-rate analysis of deterministic errors for forward-backward splitting (FBS). We then extend our analysis to biased stochastic errors, by first characterizing a family of samplers and providing a high probability bound that allows understanding not only FBS, but also proximal gradient (PG) methods. We derive some interesting conclusions: FBS requires only a logarithmically increasing number of random samples in order to converge (although at a very low rate); the required number of random samples is the same for the deterministic and the biased stochastic setting for FBS and basic PG; accelerated PG is not guaranteed to converge in the biased stochastic setting.

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Jean Honorio. 2012-06-18. Convergence Rates of Biased Stochastic Optimization for Learning Sparse Ising Models. https://arxiv.org/abs/1206.4627

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