Recent work has established an empirically successful framework for adapting
learning rates for stochastic gradient descent (SGD). This effectively removes
all needs for tuning, while automatically reducing learning rates over time on
stationary problems, and permitting learning rates to grow appropriately in
non-stationary tasks. Here, we extend the idea in three directions, addressing
proper minibatch parallelization, including reweighted updates for sparse or
orthogonal gradients, improving robustness on non-smooth loss functions, in the
process replacing the diagonal Hessian estimation procedure that may not always
be available by a robust finite-difference approximation. The final algorithm
integrates all these components, has linear complexity and is hyper-parameter
free.Comment: Published at the First International Conference on Learning
Representations (ICLR-2013). Public reviews are available at
http://openreview.net/document/c14f2204-fd66-4d91-bed4-153523694041#c14f2204-fd66-4d91-bed4-15352369404