Related papers: Nonlinear Two-Time-Scale Stochastic Approximation:…

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

We study a continuous-time approximation of the stochastic gradient descent process for minimizing the population expected loss in learning problems. The main results establish general sufficient conditions for the convergence, extending…

Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important…

In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

This paper investigates the adaptive identification and prediction problems for stochastic dynamical systems with saturated observations, which arise from various fields in engineering and social systems, but up to now still lack…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

We present two related anytime algorithms for control of nonlinear systems when the processing resources available are time-varying. The basic idea is to calculate tentative control input sequences for as many time steps into the future as…

Stochastic linearization is a method used in Quasilinear Control (QLC) to replace a nonlinearity by an equivalent gain and a bias, utilizing the statistical properties of random inputs. In this paper, the theory of stochastic linearization…

We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible…

The finite time stability (FnTSta) theory of delayed systems has not been set up until now. In this paper, we propose a two-phases-method (2PM), to achieve this object. In the first phase, we prove that the time for norm of system error…

We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…

In this paper we present a framework to analyze the asymptotic behavior of two timescale stochastic approximation algorithms including those with set-valued mean fields. This paper builds on the works of Borkar and Perkins & Leslie. The…

We develop a neural-network framework for multi-period risk--reward stochastic control problems with constrained two-step feedback policies that may be discontinuous in the state. We allow a broad class of objectives built on a…

We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…