To address this gap, we study deterministic/stochastic versions of SAM with practical configurations (i.e., constant

Suppose h ( )=e x p ( ) . M -matrix (see [ 50 ]).

The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality;

Lipschitzness, which we make precise in Section 2 and in Assumption 3.1.

Our preliminary results suggest that the regularized exponential mechanism can effectively emulate previous empirical and population risk bounds, negating the need for smoothness assumptions for algorithms with polynomial running time.

In this paper we study the second-order optimality of decentralized stochastic algorithm that escapes saddle point efficiently for nonconvex optimization problems.

Then momentum acceleration is also introduced into our dual accelerating update step.