Stochastic Approximation Algorithms

06 Apr 2023 18:36

Logically, "stochastic approximation" could refer to a great range of things, but in practice it has become something of a technical term for procedures that approximate the solution of an equation, observed through noise, or which try to minimize a function, again observed through noise. The former --- root-finding --- is sometimes known as the Robbins-Monro problem, and the latter --- minimization --- as the Kiefer-Wolfowitz problem. (Tangentially, that Wolfowitz is the father of the Wolfowitz who helped drag us into the invasion of Iraq.) This turns out to be a subject with deep connections to the theory of on-line learning algorithms and recursive estimation, which is really how I became interested in it, but I also like it nowadays because it provides some very cute, yet powerful, probability examples...