ABSTRACT
This chapter focuses on stochastic approximation methods and applications. It presents various forms of stochastic approximation algorithms and their variants, including the basic algorithms, the most general algorithms, projection and truncation procedures, algorithms with soft constraints, global stochastic approximation algorithms, continuous-time problems, and infinite dimensional problems. Then the asymptotic properties of stochastic approximation algorithms are examined by considering their convergence, rate of convergence, asymptotic efficiency, and large deviations. The asymptotic analysis is followed by the presentation of a wide range of applications to demonstrate the utility of stochastic approximation methods.
