Asymptotic Distribution of Stochastic Approximation Procedures

Asymptotic Behaviour of Truncated Stochastic Approximation procedures with Moving Bounds

Asymptotic behaviour of stochastic approximation procedures is studeded with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. In particular, the rate of convergence and asymptotic linearity are established. Main results are supplemented with corollaries to establish different sets...

Combination of Approximation and Simulation Approaches for Distribution Functions in Stochastic Networks

This paper deals with the fundamental problem of estimating the distribution function (df) of the duration of the longest path in the stochastic activity network such as PERT network. First a technique is introduced to reduce variance in Conditional Monte Carlo Sampling (CMCS). Second, based on this technique a new procedure is developed for CMCS. Third, a combined approach of simulation and ap...

Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning

In this paper, we consider the minimization of a convex objective function defined on a Hilbert space, which is only available through unbiased estimates of its gradients. This problem includes standard machine learning algorithms such as kernel logistic regression and least-squares regression, and is commonly referred to as a stochastic approximation problem in the operations research communit...

On the convergence of linear stochastic approximation procedures

Many stochastic approximation procedures result in a stochastic algorithm of the form 1 hk+l = h k + (bk A k h k ) , k for all IC = 1 , 2 , 3 . . . . . Here, { b k , IC = 1,2 ,3 , . . .} is a Rd-valued process, { Ak , IC = 1 , 2 . 3 . . . . } is a symmetric, positive semidefinite Redxd-valued process, and { h k k = 1,2 ,3 , . .} is a sequence of stochastic estimates which hopefully converges to...

Asymptotic Distribution of Divergence Measure with Applications