Feb. 13, 2024, 5:42 a.m. | Yuriy Dorn Aleksandr Katrutsa Ilgam Latypov Andrey Pudovikov

cs.LG updates on arXiv.org arxiv.org

In this study, we propose a new method for constructing UCB-type algorithms for stochastic multi-armed bandits based on general convex optimization methods with an inexact oracle. We derive the regret bounds corresponding to the convergence rates of the optimization methods. We propose a new algorithm Clipped-SGD-UCB and show, both theoretically and empirically, that in the case of symmetric noise in the reward, we can achieve an $O(\log T\sqrt{KT\log T})$ regret bound instead of $O\left (T^{\frac{1}{1+\alpha}} K^{\frac{\alpha}{1+\alpha}} \right)$ for the case …

algorithm algorithms convergence cs.lg general math.oc multi-armed bandits noise optimization oracle stat.ml stochastic study type

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