Choosing the Sample with Lowest Loss makes SGD Robust

• URL: http://arxiv.org/abs/2001.03316v1
• Date: Fri, 10 Jan 2020 05:39:17 GMT
• Title: Choosing the Sample with Lowest Loss makes SGD Robust
• Authors: Vatsal Shah, Xiaoxia Wu, Sujay Sanghavi
• Abstract summary: We propose a simple variant of the simple gradient descent (SGD) method in each step. Vanilla represents a new algorithm that is however effectively minimizing a non-current sum with the smallest loss. Our theoretical analysis of this idea for ML problems is backed up with small-scale neural network experiments.
• Score: 19.08973384659313
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The presence of outliers can potentially significantly skew the parameters of machine learning models trained via stochastic gradient descent (SGD). In this paper we propose a simple variant of the simple SGD method: in each step, first choose a set of k samples, then from these choose the one with the smallest current loss, and do an SGD-like update with this chosen sample. Vanilla SGD corresponds to k = 1, i.e. no choice; k >= 2 represents a new algorithm that is however effectively minimizing a non-convex surrogate loss. Our main contribution is a theoretical analysis of the robustness properties of this idea for ML problems which are sums of convex losses; these are backed up with linear regression and small-scale neural network experiments

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