Criteria and Convergence Rates in Noisy Optimization

International audienceIn an optimization framework, some criteria might be more relevant than others; the internal computational cost of the optimization algorithm might be negligible or not; the quality of intermediate search points might be important or not. For this reason measuring the performance of an algorithm is a delicate task. In addition, the usual criteria are often approximated for the sake of simplicity of the analysis, or for simplifying the design of test beds. This situation makes sense both in noise-free and noisy settings; however it is more often crucial in the latter case. We here discuss and compare several performance criteria published in the literature in the case of noisy optimization. We review existing rates, for various existing criteria, propose new rates, and check if some classically observed criteria are good approximations of sound criteria