Bayesian Approach to the Optimization of Adaptive Systems

This paper describes how an adaptive system can adapt itself to optimize its performance under the influence of uncertain environment. At each stage of adaptation, the uncertain environment, which is represented by a random vector with an unknown statistical property, is estimated by Bayesian approach from its past outcomes up to the latest one. This approach is investigated in general so that the probability distribution of the future outcomes of the random vector is not restricted to any particular one. For most of the adaptive systems, these probability distributions are assumed to be the same. However, in the case of signal adaptation, it is shown that the results as well as the execution of the optimization technique are alike whether or not the probability distributions of the forthcoming outcomes of the random vector are the same.