We treat an interesting class of "distributed" recursive stochastic algorithms (of the stochastic approximation type) that arises when parallel processing methods are used for the Monte Carlo optimization of systems, as well as in applications such as decentralized and asynchronous on-line optimization of the flows in communication networks. They arise generally in applications where different (noisy) processors control different components of the system state variable, and the processors compute and communicate in an asynchronous way. Since the computation and communication times are random (data and noise dependent) and asynchronous, there is no "iterate number" that is a common index for all the processors. This causes much of the analytical difficulty, and one must use elapsed processing time (the very natural alternative) rather than iterate number as the process parameter. The asymptotic properties (as the system "gain" goes to zero) are analyzed under conditions of both exogeneous noise and state d...
[1]
P. Billingsley,et al.
Convergence of Probability Measures
,
1970,
The Mathematical Gazette.
[2]
G. Papanicolaou,et al.
Stability and Control of Stochastic Systems with Wide-band Noise Disturbances. I
,
1978
.
[3]
H. Kushner,et al.
Asymptotic Properties of Stochastic Approximations with Constant Coefficients.
,
1981
.
[4]
John N. Tsitsiklis,et al.
Problems in decentralized decision making and computation
,
1984
.
[5]
Harold J. Kushner,et al.
Approximation and Weak Convergence Methods for Random Processes
,
1984
.
[6]
H. Kushner,et al.
An Invariant Measure Approach to the Convergence of Stochastic Approximations with State Dependent Noise.
,
1984
.