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arXiv · 1502.02846

Probabilistic Line Searches for Stochastic Optimization

Maren Mahsereci·Philipp Hennig
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Abstract

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent.

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Maren Mahsereci, Philipp Hennig. 2016-01-18. Probabilistic Line Searches for Stochastic Optimization. https://arxiv.org/abs/1502.02846

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