Never Go Full Batch (in Stochastic Convex Optimization)

• URL: http://arxiv.org/abs/2107.00469v1
• Date: Tue, 29 Jun 2021 16:07:50 GMT
• Title: Never Go Full Batch (in Stochastic Convex Optimization)
• Authors: Idan Amir, Yair Carmon, Tomer Koren, Roi Livni
• Abstract summary: We study the generalization performance of $textfull-batch$ optimization algorithms for convex optimization. We provide a new separation result showing that, while algorithms such as gradient descent can generalize and optimize the population risk to within $epsilon$ after $O (1/epsilon2)$, full-batch methods either need at least $Omega (1/epsilon4)$ iterations or exhibit a dimension-dependent sample complexity.
• Score: 42.46711831860667
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the generalization performance of $\text{full-batch}$ optimization algorithms for stochastic convex optimization: these are first-order methods that only access the exact gradient of the empirical risk (rather than gradients with respect to individual data points), that include a wide range of algorithms such as gradient descent, mirror descent, and their regularized and/or accelerated variants. We provide a new separation result showing that, while algorithms such as stochastic gradient descent can generalize and optimize the population risk to within $\epsilon$ after $O(1/\epsilon^2)$ iterations, full-batch methods either need at least $\Omega(1/\epsilon^4)$ iterations or exhibit a dimension-dependent sample complexity.

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