“Probabilistic Line Searches for Stochastic Optimization”, Maren Mahsereci, Philipp Hennig2015-02-10 (neural net, Bayes)⁠:

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.