Randomization methods in optimization and adaptive control

摘要

We consider simultaneous perturbation stochastic approximation (SPSA) methods applied to noise-free problems in optimization and adaptive control. More generally, we consider discrete-time fixed gain stochastic approximation processes that are defined in terms of a random field that is identically zero at some point θ{sup}*. The boundedness of the estimator process is enforced by a resetting mechanism. Under appropriate technical conditions the estimator sequence converges toθ{sup}* with geometric rate almost surely. This result is in striking contrast to classical stochastic approximation theory where the typical convergence rate is n{sup}(-1/2). For the proof a discrete-time version of the ODE-method is used and the techniques of [10] are extended. A simple variant of noise free-SPSA is applied to extend a direct controller tuning method named Iterative Feedback Tuning (IFT), see [16]. Using randomization, the number of experiments required to obtain an unbiased estimate of the gradient of the cost function can be reduced significantly for multi-input multi-output systems.