For the linear bandit problem, we extend the analysis of algorithm CombEXP from [R. Combes, M. S. Talebi Mazraeh Shahi, A. Proutiere, and M. Lelarge. Combinatorial bandits revisited. In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett, editors, Advances in Neural Information Processing Systems 28, pages 2116--2124. Curran Associates, Inc., 2015. URL http://papers.nips.cc/paper/5831-combinatorial-bandits-revisited.pdf] to the high-probability case against adaptive adversaries, allowing actions to come from an arbitrary polytope. We prove a high-probability regret of \(O(T^{2/3})\) for time horizon \(T\). While this bound is weaker than the optimal \(O(\sqrt{T})\) bound achieved by GeometricHedge in [P. L. Bartlett, V. Dani, T. Hayes, S. Kakade, A. Rakhlin, and A. Tewari. High-probability regret bounds for bandit online linear optimization. In 21th Annual Conference on Learning Theory (COLT 2008), July 2008. http://eprints.qut.edu.au/45706/1/30-Bartlett.pdf], CombEXP is computationally efficient, requiring only an efficient linear optimization oracle over the convex hull of the actions.

翻译：对于线性土匪问题,我们将对CombEXP算法的分析从[R.Combes、M.S.Talebi Mazraeh Shahi、A.Proutiere和M.Legraf. Legrapher.]扩大到针对适应性对手的高概率案例,允许从任意的多功能中采取行动。在C. Cortes、N.D. Lawrence、D. D. Lee、M. Sugiyama和R. Garnett编辑、神经信息处理系统进步28页,第2116-2124页。Curran Associates, Incional http://papers.nips.cc/paper 5831-combinator-britits-revisit.pdf],再扩展至允许行动来自任意的多功能。我们证明,对于时间前景来说,(O(T&2/3)M.