Stochastic convex optimization with bandit feedback
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Abstract
This paper addresses the problem of minimizing a convex, Lipschitz function f over a convex, compact set X under a stochastic bandit feedback model. In this model, the algorithm is allowed to observe noisy realizations of the function value f (x) at any query point 
We demonstrate a generalization of the ellipsoid algorithm that incurs 
re-gret. Since any algorithm has regret at least 
on this problem, our algorithm is optimal in terms of the scaling with T .
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