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I will present a new theoretical perspective on two basic problems arising in stochastic optimization. The first one is arguably the most elementary problem in stochastic optimization: assume that one wants to find the maximum of function defined on a finite set, and that one is given a budget of n noisy evaluations. What is the best sequential allocation procedure for the evaluations? The second problem that I will discuss is inspired from the issue of security analysis of a power system. We formalize this problem as follows: Let X be a set, and A a subset of X of interesting elements in X. One can access X only through requests to a finite set of probabilistic experts. More precisely, when one makes a request to the i^th expert, the latter draws independently at random a point from a fixed probability distribution P_i over X. One is interested in discovering rapidly as many elements of A as possible, by making sequential requests to the experts.
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