Bandit-style algorithms have been studied extensively in stochastic and adversarial settings. Such algorithms have been shown to be useful in multiplayer settings, e.g. to solve the wireless network selection problem, which can be formulated as an adversarial bandit problem. A leading bandit algorithm for the adversarial setting is EXP3. However, network behavior is often repetitive, where user density and network behavior follow regular patterns. Bandit algorithms, like EXP3, fail to provide good guarantees for periodic behaviors. A major reason is that these algorithms compete against fixed-action policies, which is ineffective in a periodic setting. In this paper, we define a periodic bandit setting, and periodic regret as a better performance measure for this type of setting. Instead of comparing an algorithm's performance to fixed-action policies, we aim to be competitive with policies that play arms under some set of possible periodic patterns $F$ (for example, all possible periodic functions with periods $1,2,\cdots,P$). We propose Periodic EXP4, a computationally efficient variant of the EXP4 algorithm for periodic settings. With $K$ arms, $T$ time steps, and where each periodic pattern in $F$ is of length at most $P$, we show that the periodic regret obtained by Periodic EXP4 is at most $O\big(\sqrt{PKT \log K + KT \log |F|}\big)$. We also prove a lower bound of $\Omega\big(\sqrt{PKT + KT \frac{\log |F|}{\log K}} \big)$ for the periodic setting, showing that this is optimal within log-factors. As an example, we focus on the wireless network selection problem. Through simulation, we show that Periodic EXP4 learns the periodic pattern over time, adapts to changes in a dynamic environment, and far outperforms EXP3.

本文介绍了带周期模式的波动策略，该策略可以应用于无线网络选择问题。我们提出了一种计算上有效的算法 Periodic EXP4，该算法采用周期性遗憾作为更好的绩效度量，并在模拟中证明了其效率和比 EXP3 优良的特点。

周期性赌博机与无线网络选择