一种针对线性赌博机的高效高概率算法
摘要
针对线性赌博机问题，我们将 CombEXP 算法的分析 [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] 扩展到对抗自适应对手的高概率情形，并允许动作来自任意多面体。我们证明了对于时间范围 T，高概率遗憾界为 O(T^{2/3})。虽然此界弱于 GeometricHedge 在 [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] 中达到的最优 O(√T) 界，但 CombEXP 计算效率高，仅需一个对动作凸包的高效线性优化预言机。
引用
@article{arxiv.1610.02072,
title = {An efficient high-probability algorithm for Linear Bandits},
author = {Gábor Braun and Sebastian Pokutta},
journal= {arXiv preprint arXiv:1610.02072},
year = {2016}
}
备注
17 pages