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A Best-of-Both-Worlds Proof for Tsallis-INF without Fenchel Conjugates

arXiv 2511.11211 ↗First posted 14 Nov 2025cs.LG math.OC stat.MLcited by 0

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Abstract (arXiv)

In this short note, we present a simple derivation of the best-of-both-world guarantee for the Tsallis-INF multi-armed bandit algorithm from J. Zimmert and Y. Seldin. Tsallis-INF: An optimal algorithm for stochastic and adversarial bandits. Journal of Machine Learning Research, 22(28):1-49, 2021. URL https://jmlr.csail.mit.edu/papers/volume22/19-753/19-753.pdf. In particular, the proof uses modern tools from online convex optimization and avoid the use of conjugate functions. Also, we do not optimize the constants in the bounds in favor of a slimmer proof.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 2 of its 9 references that are in the map. First posted on arXiv 14 Nov 2025.

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References · 2

  1. 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 412
  2. 2018Tsallis-INF: An Optimal Algorithm for Stochastic and Adversarial Banditscited by 123

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