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We consider the problem of finding a saddle point for the convex-concave objective minxmaxyf(x)+⟨Ax,y⟩−g∗(y), where f is a convex function with locally Lipschitz gradient and g is convex and possibly non-smooth. We propose an ...
We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...
We propose a class of novel variance-reduced stochastic conditional gradient methods. By adopting the recent stochastic path-integrated differential estimator technique (SPIDER) of Fang et al. (2018) for the classical Frank-Wolfe (FW) method, we introduce ...
It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...
This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...
This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to t ...
We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...
It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and—in asynchronous implementations—on the gradient staleness. Especially, it has been observed that the spe ...
Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalize ...
We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-funct ...
