论文标题
与一般图形反馈一起学习随机和对抗性匪徒
Simultaneously Learning Stochastic and Adversarial Bandits with General Graph Feedback
论文作者
论文摘要
通过图形反馈的在线学习问题已经在文献中进行了广泛的研究，因为它的一般性和对各种学习任务进行建模的潜力。现有作品主要研究对抗性和随机反馈。如果对反馈机制的先验知识是不可用的或错误的，那么这种专门设计的算法可能会遭受巨大的损失。为了避免此问题，\ citet {ererez2021towards}尝试针对这两个环境进行优化。但是，他们认为反馈图是无方向性的，并且每个顶点都有一个自动循环，这会损害框架的一般性，并且在应用程序中可能无法满足。有了一般的反馈图，在拉动该手臂时可能无法观察到手臂，这使得探索更加昂贵，并且在这两种环境中表现最佳的算法更具挑战性。在这项工作中，我们通过新的权衡机制克服了这一困难，并以精心设计的探索和剥削比例克服了这一困难。 We prove the proposed algorithm simultaneously achieves $\mathrm{poly} \log T$ regret in the stochastic setting and minimax-optimal regret of $\tilde{O}(T^{2/3})$ in the adversarial setting where $T$ is the horizon and $\tilde{O}$ hides parameters independent of $T$ as well as对数术语。据我们所知，这是通用反馈图的第一个最佳世界结果。
The problem of online learning with graph feedback has been extensively studied in the literature due to its generality and potential to model various learning tasks. Existing works mainly study the adversarial and stochastic feedback separately. If the prior knowledge of the feedback mechanism is unavailable or wrong, such specially designed algorithms could suffer great loss. To avoid this problem, \citet{erez2021towards} try to optimize for both environments. However, they assume the feedback graphs are undirected and each vertex has a self-loop, which compromises the generality of the framework and may not be satisfied in applications. With a general feedback graph, the observation of an arm may not be available when this arm is pulled, which makes the exploration more expensive and the algorithms more challenging to perform optimally in both environments. In this work, we overcome this difficulty by a new trade-off mechanism with a carefully-designed proportion for exploration and exploitation. We prove the proposed algorithm simultaneously achieves $\mathrm{poly} \log T$ regret in the stochastic setting and minimax-optimal regret of $\tilde{O}(T^{2/3})$ in the adversarial setting where $T$ is the horizon and $\tilde{O}$ hides parameters independent of $T$ as well as logarithmic terms. To our knowledge, this is the first best-of-both-worlds result for general feedback graphs.
