Incremental Without Replacement Sampling in Nonconvex Optimization
Edouard Pauwels · Journal of Optimization Theory and Applications · 2021
Minibatch decomposition methods for empirical risk minimization are commonly analyzed in a stochastic approximation setting, also known as sampling with replacement. On the other hand, modern implementations of such techniques are incremental: they rely on sampling without replacement, for which available analysis is much scarcer. We provide convergence guaranties for the latter variant by analyzing a versatile incremental gradient scheme. For this scheme, we consider constant, decreasing or adaptive step sizes. In the smooth setting, we obtain explicit complexity estimates in terms of epoch counter. In the nonsmooth setting, we prove that the sequence is attracted by solutions of optimality conditions of the problem.