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13
Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation
 IEEE Transactions on Automatic Control
, 1992
"... Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root. This p ..."
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Cited by 213 (14 self)
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Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root. This paper presents an SA algorithm that is based on a "simultaneous perturbation" gradient approximation instead of the standard finite difference approximation of KieferWolfowitz type procedures. Theory and numerical experience indicate that the algorithm presented here can be significanfiy more efficient than the standard finite differencebased algorithms in largedimensional problems.
Stochastic Power Control for Cellular Radio Systems
 IEEE Trans. Commun
, 1997
"... For wireless communication systems, iterative power control algorithms have been proposed to minimize transmitter powers while maintaining reliable communication between mobiles and base stations. To derive deterministic convergence results, these algorithms require perfect measurements of one or mo ..."
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Cited by 89 (8 self)
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For wireless communication systems, iterative power control algorithms have been proposed to minimize transmitter powers while maintaining reliable communication between mobiles and base stations. To derive deterministic convergence results, these algorithms require perfect measurements of one or more of the following parameters: (i) the mobile's signal to interference ratio (SIR) at the receiver, (ii) the interference experienced by the mobile, and (iii) the bit error rate. However, these quantities are often difficult to measure and deterministic convergence results neglect the effect of stochastic measurements. In this work, we develop distributed iterative power control algorithms that use readily available measurements. Two classes of power control algorithms are proposed. Since the measurements are random, the proposed algorithms evolve stochastically and we define the convergence in terms of the mean squared error (MSE) of the power vector from the optimal power vector that is t...
Optimization via simulation: a review
 Annals of Operations Research
, 1994
"... We review techniques for optimizing stochastic discreteevent systems via simulation. We discuss both the discrete parameter case and the continuous parameter case, but concentrate on the latter which has dominated most of the recent research in the area. For the discrete parameter case, we focus on ..."
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Cited by 67 (20 self)
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We review techniques for optimizing stochastic discreteevent systems via simulation. We discuss both the discrete parameter case and the continuous parameter case, but concentrate on the latter which has dominated most of the recent research in the area. For the discrete parameter case, we focus on the techniques for optimization from a finite set: multiplecomparison procedures and rankingandselection procedures. For the continuous parameter case, we focus on gradientbased methods, including perturbation analysis, the likelihood ratio method, and frequency domain experimentation. For illustrative purposes, we compare and contrast the implementation of the techniques for some simple discreteevent systems such as the (s, S) inventory system and the GI/G/1 queue. Finally, we speculate on future directions for the field, particularly in the context of the rapid advances being made in parallel computing.
Almost Sure Approximations to the RobbinsMonro and KieferWolfowitz Processes with Dependent Noise
"... We study a recursive algorithm which includes the multidimensional RobbinsMonro and KieferWolfowitz processes. The assumptions on the disturbances are weaker than the usual assumption that they be a martingale difference sequence. It is shown that the algorithm can be represented as a weighted ave ..."
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Cited by 14 (0 self)
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We study a recursive algorithm which includes the multidimensional RobbinsMonro and KieferWolfowitz processes. The assumptions on the disturbances are weaker than the usual assumption that they be a martingale difference sequence. It is shown that the algorithm can be represented as a weighted average of the disturbances. This representation can be used to prove asymptotic results for stochastic approximation procedures. As an example, we approximate the one dimensional KieferWolfowitz process almost surely by Brownian motion, and as a byproduct obtain a law of the iterated logarithm.
Weighted averaging and stochastic approximation
 Math. Control Signals Systems
, 1997
"... We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a samplepath analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated n ..."
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Cited by 5 (2 self)
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We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a samplepath analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and su cient noiseconditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the standalone stochastic approximation algorithms.
Some averaging and stability results for random differential equations
 SIAM Journal of Applied Mathematics
, 1979
"... Abstract. This paper concerns differential equations which contain strongly mixing random processes (processes for which the "past " and the "future " are asymptotically independent). When the "rate " of mixing is rapid relative to the rate of change of the solution process, information about the be ..."
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Cited by 5 (0 self)
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Abstract. This paper concerns differential equations which contain strongly mixing random processes (processes for which the "past " and the "future " are asymptotically independent). When the "rate " of mixing is rapid relative to the rate of change of the solution process, information about the behavior of the solution is obtained. Roughly, the results fall into three categories: 1. Quite generally, the solution process is well approximated by a deterministic trajectory, over a finite time interval. 2. For more restricted systems, this approximation extends to the infinite interval [0,). 3. Conditions for the asymptotic stability of 2 Ax, where A is an n n matrixvalued random process, are obtained. 1. Introduction. We
Selfish response to epidemic propagation
, 2011
"... An epidemic that spreads in a network calls for a decision on the part of the network users. They have to decide whether to protect themselves or not. Their decision depends on the tradeoff between the perceived infection and the protection cost. Aiming to help users reach an informed decision, sec ..."
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Cited by 4 (1 self)
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An epidemic that spreads in a network calls for a decision on the part of the network users. They have to decide whether to protect themselves or not. Their decision depends on the tradeoff between the perceived infection and the protection cost. Aiming to help users reach an informed decision, security advisories provide periodic information about the infection level in the network. We study the bestresponse dynamic in a network whose users repeatedly activate or deactivate security, depending on what they learn about the infection level. Our main result is the counterintuitive fact that the equilibrium level of infection increases as the users â€™ learning rate increases. The same is true when the users follow smooth bestresponse dynamics, or any other continuous response function that implies higher probability of protection when learning a higher level of infection. In both cases, we characterize the stability and the domains of attraction of the equilibrium points. Our finding also holds when the epidemic propagation is simulated on human contact traces, both when all users are of the same bestresponse behavior type and when they are of two distinct behavior types. 1
CONVERGENCE RATE AND AVERAGING OF NONLINEAR TWOTIMESCALE STOCHASTIC APPROXIMATION ALGORITHMS
, 2006
"... The first aim of this paper is to establish the weak convergence rate of nonlinear twotimescale stochastic approximation algorithms. Its second aim is to introduce the averaging principle in the context of twotimescale stochastic approximation algorithms. We first define the notion of asymptotic ..."
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Cited by 3 (0 self)
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The first aim of this paper is to establish the weak convergence rate of nonlinear twotimescale stochastic approximation algorithms. Its second aim is to introduce the averaging principle in the context of twotimescale stochastic approximation algorithms. We first define the notion of asymptotic efficiency in this framework, then introduce the averaged twotimescale stochastic approximation algorithm, and finally establish its weak convergence rate. We show, in particular, that both components of the averaged twotimescale stochastic approximation algorithm simultaneously converge at the optimal rate n.
A Representation Theorem of Generalized RobbinsMonro Processes and Applications
"... Many generalizations of the RobbinsMonro process have been proposed for the purpose of recursive estimation. In this paper, it is shown that for a large class of such processes, the estimator can be represented as a stun of possibly dependent random variables, and therefore the asymptotic behavior ..."
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Many generalizations of the RobbinsMonro process have been proposed for the purpose of recursive estimation. In this paper, it is shown that for a large class of such processes, the estimator can be represented as a stun of possibly dependent random variables, and therefore the asymptotic behavior of the estimate can be studied using limit theorems for stunS. Two applications are considered: robust recursive estimation for autoregressive processes and recursive nonlinear regression.