Incremental Without Replacement Sampling in Nonconvex Optimization

Edouard Pauwels (1)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are incremental: they rely on sampling without replacement, for which available analysis are much scarcer. We provide convergence guaranties for the latter variant by analysing 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.

Keywords: Without Replacement Sampling; Incremental Methods; Nonconvex Optimization; First order Methods; Stochastic Gradient; Adaptive Methods; Backpropagation; Deep Learning

Domains: Optimization and Control [math.OC]; Machine Learning [cs.LG]

Edouard Pauwels. Incremental Without Replacement Sampling in Nonconvex Optimization. Journal of Optimization Theory and Applications, 2021, ⟨10.1007/s10957-021-01883-2⟩. ⟨hal-02896102v4⟩