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arXiv Machine Learning By Mohammad Pedramfar, Siamak Ravanbakhsh

The Tilted Sampling Problem: Optimism, Posterior Sampling, and Logarithmic Regret

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The paper introduces the tilted sampling problem, where an online learner aims to sample from a Gibbs distribution defined by an unknown reward function. It defines sampling regret as the temperature‑normalized cumulative KL divergence between the learner’s distribution and the target Gibbs distribution, linking it to entropy‑regularized reward maximization. The authors develop sampling analogues of UCB and Thompson sampling, proving that sampling regret can achieve logarithmic growth in time, unlike standard regret which scales as ×O(√T).

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