新证明让Tsallis-INF算法在随机与对抗环境中均表现最优，无需复杂数学工具。
A Best-of-Both-Worlds Proof for Tsallis-INF without Fenchel Conjugates
- 用在线凸优化新方法推导，避开传统共轭函数
- 保持算法在两类环境下的最优性能保证
- 适合关注算法简洁性与理论深度的研究者
本文提供了一个简洁的推导，证明了Tsallis-INF多臂赌博机算法在随机与对抗环境下的最优双世界性能。该证明采用现代在线凸优化工具，避免使用共轭函数，且未对边界常数进行优化，以换取更简洁的证明结构。结果表明，该算法能在两种典型设置下同时实现最优遗憾界。
原文摘要 · Abstract (English)
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.
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