Stochastic Optimization

Stochastic optimization algorithms have been growing rapidly in popularity over the last decade or two, with a number of methods now becoming “industry standard ” approaches for solving challenging optimization problems. This chapter provides a synopsis of some of the critical issues associated with stochastic optimization and a gives a summary of several popular algorithms. Much more complete discussions are available in the indicated references. To help constrain the scope of this article, we restrict our attention to methods using only measurements of the criterion (loss function). Hence, we do not cover the many stochastic methods using information such as gradients of the loss function. Section 1 discusses some general issues in stochastic optimization. Section 2 discusses random search methods, which are simple and surprisingly powerful in many applications. Section 3 discusses stochastic approximation, which is a foundational approach in stochastic optimization. Section 4 discusses a popular method that is based on connections to natural evolution—genetic algorithms. Finally, Section 5 offers some concluding remarks