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Bandit Smooth Convex Optimization: Improving the Bias-Variance Tradeoff
Ofer Dekel · Ronen Eldan · Tomer Koren

Wed Dec 09 07:10 AM -- 07:35 AM (PST) @ Room 210 A
Bandit convex optimization is one of the fundamental problems in the field of online learning. The best algorithm for the general bandit convex optimization problem guarantees a regret of $\widetilde{O}(T^{5/6})$, while the best known lower bound is $\Omega(T^{1/2})$. Many attemptshave been made to bridge the huge gap between these bounds. A particularly interesting special case of this problem assumes that the loss functions are smooth. In this case, the best known algorithm guarantees a regret of $\widetilde{O}(T^{2/3})$. We present an efficient algorithm for the banditsmooth convex optimization problem that guarantees a regret of $\widetilde{O}(T^{5/8})$. Our result rules out an $\Omega(T^{2/3})$ lower bound and takes a significant step towards the resolution of this open problem.

Author Information

Ofer Dekel (Microsoft Research)
Ronen Eldan (Weizmann)
Tomer Koren (Technion)

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