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arXiv · 1610.05022

Sparse Accelerated Exponential Weights

Pierre Gaillard·Olivier Wintenberger
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Abstract

We consider the stochastic optimization problem where a convex function is minimized observing recursively the gradients. We introduce SAEW, a new procedure that accelerates exponential weights procedures with the slow rate $1/\sqrt{T}$ to procedures achieving the fast rate $1/T$. Under the strong convexity of the risk, we achieve the optimal rate of convergence for approximating sparse parameters in $\mathbb{R}^d$. The acceleration is achieved by using successive averaging steps in an online fashion. The procedure also produces sparse estimators thanks to additional hard threshold steps.

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Pierre Gaillard, Olivier Wintenberger. 2016-10-17. Sparse Accelerated Exponential Weights. https://arxiv.org/abs/1610.05022

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