Multi-armed bandit problems are the most basic examples of sequential decision problems
with an exploration-exploitation trade-off. This is the balance between staying with the option …

In this paper, we introduce a new stochastic approximation type algorithm, namely, the
randomized stochastic gradient (RSG) method, for solving an important class of nonlinear …

In this paper we consider optimization problems where the objective function is given in a
form of the expectation. A basic difficulty of solving such stochastic optimization problems is …

We consider regularized stochastic learning and online optimization problems, where the
objective function is the sum of two convex terms: one is the loss function of the learning …

This paper considers an important class of convex programming (CP) problems, namely, the
stochastic composite optimization (SCO), whose objective function is given by the …

In this paper we present a generic algorithmic framework, namely, the accelerated stochastic
approximation (AC-SA) algorithm, for solving strongly convex stochastic composite …

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic
optimization, where we assume that noisy information about the gradients of the objective …

This paper studies statistical aggregation procedures in the regression setting. A motivating
factor is the existence of many different methods of estimation, leading to possibly competing …

This paper is a selective review of the regularization methods scattered in statistics literature.
We introduce a general conceptual approach to regularization and fit most existing methods …

We study the problem of aggregation under the squared loss in the model of regression with
deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via …