In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being over n agents having access only to zeroth-order (ZO) information of cost. This has various machine learning applications. As solution, propose two ZO algorithms, in which at each iteration agent samples local oracle points time-varying smoothing parameter. We show that proposed algor...

In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality (VI) problems: extra-point scheme and extra-momentum scheme. The first one is a general based on updating iterative sequence an auxiliary sequence. case of deterministic VI model, approach includes several state-of-the-art first-order methods as its special cases. second combines ...

We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve problems with only noisy objective function evaluations. Toward this, our main contribution propose estimators of gradient and Hessian from evaluations, based on a version Gaussian smoothing technique. The proposed overcome difficulty nonlinearity manifold constr...

In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H2-optimal deterministic systems. particular, supplement complete theory error bounds differential equations. With these bounds, establish a link between output (with additive multiplicative noise) modified versions H2-norm both bilinear When deriving respective optimality conditions minimizin...