Adaptive stochastic approximations

Many of the present problems in automatic control economic systems and living organism can be converted to parameter optimization in stochastic systems. foremost among these problems are questions of the control of systems with incomplete information, learning problems, adaptive control, identification of objects, and the automatic synthesis of objects. such problems can be solved by stochastic approximation methods which are, essentially, iterative procedures. for this reason, great attention is paid to these methods in connection with practical applications. they were elaborated as a purely mathematical problem a long time ago and a number of valuable results are now available. not only the conditions of convergence,but some properties of the asymptotic speed of convergence are also known. in some cases, however, a disadvantage of stochastic approximations is the slow convergence to the desired extreme of the optimality criterion. at present, utmost attention is devoted to the elimination of these undesirable properties. unfortunately, practical requirements are often in disagreement with the assumptions from which we start when seeking more effective algorithms. (...);