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Recent work has established an empirically successful framework for adaptinglearning rates for stochastic gradient descent (SGD). This effectively removesall needs for tuning, while automatically reducing learning rates over time onstationary problems, and permitting learning rates to grow appropriately innon-stationary tasks. Here, we extend the idea in three directions, addressingproper minibatch parallelization, including reweighted updates for sparse ororthogonal gradients, improving robustness on non-smooth loss functions, in theprocess replacing the diagonal Hessian estimation procedure that may not alwaysbe available by a robust finite-difference approximation. The final algorithmintegrates all these components, has linear complexity and is hyper-parameterfree.

Adaptive learning rates and parallelization for stochastic, sparse, non-smooth gradients