In this paper we present the greedy step averaging(GSA) method, a parameter-free stochastic optimization algorithm for a variety of machine learning problems. As a gradient-based optimization method, GSA makes use of the information from the minimizer of a single sample's loss function, and takes average strategy to calculate reasonable learning rate sequence. While most existing gradient-based algorithms introduce an increasing number of hyper parameters or try to make a trade-off between computational cost and convergence rate, GSA avoids the manual tuning of learning rate and brings in no more hyper parameters or extra cost. We perform exhaustive numerical experiments for logistic and softmax regression to compare our method with the other state of the art ones on 16 datasets. Results show that GSA is robust on various scenarios.
In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG and SVRG, with better theoretical convergence rates, and has support for composite objectives where a proximal operator is used on the regulariser. Unlike SDCA, SAGA supports non-strongly convex problems directly, and is adaptive to any inherent strong convexity of the problem. We give experimental results showing the effectiveness of our method.