Descriptif

This course presents both theoretical and numerical aspects of decision problems with uncertainty, where one sets a probabilistic framework in order to minimize the expectation of a cost.  Two directions are explored:
- we investigate the so-called "open-loop" situation, that is, the case where decisions do not depend on information available for the problem, and we thoroughly study the stochastics gradient method and its variants,
- we also study "closed-loop" optimization problems, that is, the case where decisions are based on partial information (often corresponding to measurements made in the past when facing an unknown future).

Such problems are of course well-motivated by decisions problems in the industry.  They also have a deep mathematical content, especially in the dynamic case when only the past information is available.  In this setting the decision is a function in a high dimensional space and therefore the numerical aspects also are challenging.

This course is part of the M2 Optimization program (Paris-Saclay University). It is given in English.