在非平稳信道下,用强化学习方法最小化队列长度的累积损失。
Minimizing Queue Length Regret for Arbitrarily Varying Channels
- 设计弱自适应多臂赌博机算法应对动态信道调度问题。
- 理论证明队列长度后悔值可被控制在约 √N × T^(3/4) 阶。
- 无需稳定队列或流量假设,适用于极端不稳定场景。
我们研究单个发送-接收对在 N 个任意变化无线信道下的在线信道调度问题。信道速率可能非平稳,且受一个盲目对手控制。每时隙,无限容量的数据队列中到达新数据;调度器在不知当前信道速率的情况下选择一个信道传输,仅在时隙结束后获知所选信道的实际速率。目标是最小化队列长度后悔值,即在线策略在时间 T 内的队列长度与始终选择最优信道(事后视角)的差距。本文提出一种弱自适应多臂赌博机(MAB)算法来最小化该后悔值。不同于以往工作,本研究不假设队列或到达过程稳定,因此结果在队列不稳定时依然成立。核心观察是:队列长度后悔可被上界为一个统一覆盖所有子区间 [T] 的 MAB 策略的后悔值。作为技术贡献,我们提出一种弱自适应对抗性 MAB 算法,在高概率下实现 Õ(√N T^{3/4}) regret,从而导出相同阶的队列长度后悔界。
原文摘要 · Abstract (English)
We consider an online channel scheduling problem for a single transmitter-receiver pair equipped with $N$ arbitrarily varying wireless channels. The transmission rates of the channels might be non-stationary and could be controlled by an oblivious adversary. At every slot, incoming data arrives at an infinite-capacity data queue located at the transmitter. A scheduler, which is oblivious to the current channel rates, selects one of the $N$ channels for transmission. At the end of the slot, the scheduler only gets to know the transmission rate of the selected channel. The objective is to minimize the queue length regret, defined as the difference between the queue length at some time $T$ achieved by an online policy and the queue length obtained by always transmitting over the single best channel in hindsight. We propose a weakly adaptive Multi-Armed Bandit (MAB) algorithm for minimizing the queue length regret in this setup. Unlike previous works, we do not make any stability assumptions about the queue or the arrival process. Hence, our result holds even when the queueing process is unstable. Our main observation is that the queue length regret can be upper bounded by the regret of a MAB policy that competes against the best channel in hindsight uniformly over all sub-intervals of $[T]$. As a technical contribution of independent interest, we then propose a weakly adaptive adversarial MAB policy which achieves $\tilde{O}(\sqrt{N}T^{\frac{3}{4}})$ regret with high probability, implying the same bound for queue length regret.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。