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arXiv · 1806.00458

Improved Sample Complexity for Stochastic Compositional Variance Reduced Gradient

Tianyi Lin·Chenyou Fan·Mengdi Wang·Michael I. Jordan
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Abstract

Convex composition optimization is an emerging topic that covers a wide range of applications arising from stochastic optimal control, reinforcement learning and multi-stage stochastic programming. Existing algorithms suffer from unsatisfactory sample complexity and practical issues since they ignore the convexity structure in the algorithmic design. In this paper, we develop a new stochastic compositional variance-reduced gradient algorithm with the sample complexity of $O((m+n)\log(1/\epsilon)+1/\epsilon^3)$ where $m+n$ is the total number of samples. Our algorithm is near-optimal as the dependence on $m+n$ is optimal up to a logarithmic factor. Experimental results on real-world datasets demonstrate the effectiveness and efficiency of the new algorithm.

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Tianyi Lin, Chenyou Fan, Mengdi Wang, Michael I. Jordan. 2018-06-01. Improved Sample Complexity for Stochastic Compositional Variance Reduced Gradient. https://arxiv.org/abs/1806.00458

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