To this end, high-probability guarantees have been considered in the literature [35, 64, 20, 32, 22]. These results allow to control the risk associated with the worst-case tail events as theyspecify howmanyiterations would be sufficient toensureG(xk,yk) issufficiently small foranygivenfailure probability q (0,1).

We propose a generalized variant of Frank-Wolfe algorithm for solving a class ofsparse/low-rank optimization problems.

In this paper, we introduce alowrank interaction and sparse additive effects(LORIS) model which combines matrix regression on a dictionary and low-rank design, to estimate main effects andinteractions simultaneously.

One of the main reasons for their extensive applicability is that they comprise a flexible optimization framework which can simultaneously account for loss function minimization, saddle-point, game-theoretic, and fixed point problems.

This is an idealization of the usual way to train neural networks with a large hidden layer.

Most of the existing work [2, 5, 6, 7, 8] for nonconvex SCO problem is based on the assumption that both functionsf()andg()are smooth.

We assume that the lower-level objective functiong is convex but notstrongly convex,sothelower-levelproblem mayhavemultiple optimal solutions.

However, the optimization aspect is not sufficient to achieve the success of stochastic minimax optimizationinmachinelearning.

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare.

Weight matrix and connectivity measure.Assumencomputing nodes are connected by some