Stochastic convex optimization with bandit feedback

Code

• github.com/jw3479/exogenous_mdps
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Abstract

This paper addresses the problem of minimizing a convex, Lipschitz function f over a convex, compact set 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 x . The quantity of interest is the regret of the algorithm, which is the sum of the function values at algorithm's query points minus the optimal function value. We demonstrate a generalization of the ellipsoid algorithm that incurs ((d)T) regret. Since any algorithm has regret at least (T) on this problem, our algorithm is optimal in terms of the scaling with T.

Reproductions