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The Implicitly Normalized Forecaster (INF) algorithm is considered to be anoptimal solution for adversarial multi-armed bandit (MAB) problems. However,most of the existing complexity results for INF rely on restrictiveassumptions, such as bounded rewards. Recently, a related algorithm wasproposed that works for both adversarial and stochastic heavy-tailed MABsettings. However, this algorithm fails to fully exploit the available data.  In this paper, we propose a new version of INF called the ImplicitlyNormalized Forecaster with clipping (INF-clip) for MAB problems withheavy-tailed reward distributions. We establish convergence results under mildassumptions on the rewards distribution and demonstrate that INF-clip isoptimal for linear heavy-tailed stochastic MAB problems and works well fornon-linear ones. Furthermore, we show that INF-clip outperforms thebest-of-both-worlds algorithm in cases where it is difficult to distinguishbetween different arms.

Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits