Probabilistic Line Searches for Stochastic Optimization
This addresses the problem of tuning learning rates in stochastic gradient descent for machine learning practitioners, offering a novel solution that is incremental in its hybrid approach.
The paper tackles the lack of a direct equivalent to line searches in stochastic optimization by constructing a probabilistic line search that combines deterministic methods with Bayesian optimization, resulting in an algorithm that effectively removes the need to define a learning rate for stochastic gradient descent with very low computational cost and no user-controlled parameters.
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.