TY - GEN
T1 - Incremental Robbins-Monro gradient algorithm for regression in sensor networks
AU - Sundhar Ram, S.
AU - Veeravalli, V. V.
AU - Nedić, A.
PY - 2007
Y1 - 2007
N2 - We consider a network of sensors deployed to sense a spatial field for the purposes of parameter estimation. Each sensor makes a sequence of measurements that is corrupted by noise. The estimation problem is to determine the value of a parameter that minimizes a cost that is a function of the measurements and the unknown parameter. The cost function is such that it can be written as the sum of functions (one corresponding to each sensor), each of which is associated with one sensor's measurements. Such a cost function is of interest in regression. We are interested in solving the resulting optimization problem in a distributed and recursive manner. Towards this end, we combine the incremental gradient approach with the Robbins-Monro approximation algorithm to develop the Incremental Robbins-Monro Gradient (IRMG) algorithm. We investigate the convergence of the algorithm under a convexity assumption on the cost function and a stochastic model for the sensor measurements. In particular, we show that if the observations at each are independent and identically distributed, then the IRMG algorithm converges to the optimum solution almost surely as the number of observations goes to infinity. We emphasize that the IRMG algorithm itself requires no information about the stochastic model.
AB - We consider a network of sensors deployed to sense a spatial field for the purposes of parameter estimation. Each sensor makes a sequence of measurements that is corrupted by noise. The estimation problem is to determine the value of a parameter that minimizes a cost that is a function of the measurements and the unknown parameter. The cost function is such that it can be written as the sum of functions (one corresponding to each sensor), each of which is associated with one sensor's measurements. Such a cost function is of interest in regression. We are interested in solving the resulting optimization problem in a distributed and recursive manner. Towards this end, we combine the incremental gradient approach with the Robbins-Monro approximation algorithm to develop the Incremental Robbins-Monro Gradient (IRMG) algorithm. We investigate the convergence of the algorithm under a convexity assumption on the cost function and a stochastic model for the sensor measurements. In particular, we show that if the observations at each are independent and identically distributed, then the IRMG algorithm converges to the optimum solution almost surely as the number of observations goes to infinity. We emphasize that the IRMG algorithm itself requires no information about the stochastic model.
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U2 - 10.1109/CAMSAP.2007.4498027
DO - 10.1109/CAMSAP.2007.4498027
M3 - Conference contribution
AN - SCOPUS:50249131938
SN - 9781424417148
T3 - 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMPSAP
SP - 309
EP - 312
BT - 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMPSAP
T2 - 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMPSAP
Y2 - 12 December 2007 through 14 December 2007
ER -