An introspective on the Retrospective-Approximation paradigm

Retrospective Approximation (RA) is a solution paradigm introduced in the early 1990s by Chen and Schmeiser for solving one-dimensional stochastic root finding problems (SRFPs). The RA paradigm can be thought of as a refined and implementable version of sample average approximation, where a sequence of approximate problems are strategically generated and solved to identify iterates that progressively approach the desired solution. While originally aimed at one-dimensional SRFPs, the paradigm´s broader utility, particularly within general simulation optimization algorithms, is becoming increasingly evident. We discuss the RA paradigm, demonstrate its usefulness, present the key results and papers on the topic over the last fifteen years, and speculate fruitful future directions.