We consider the problem of service hosting where a service provider can dynamically rent edge resources via short term contracts to ensure better quality of service to its customers. The service can also be partially hosted at the edge, in which case, customers' requests can be partially served at the edge. The total cost incurred by the system is modeled as a combination of the rent cost, the service cost incurred due to latency in serving customers, and the fetch cost incurred as a result of the bandwidth used to fetch the code/databases of the service from the cloud servers to host the service at the edge. In this paper, we compare multiple hosting policies with regret as a metric, defined as the difference in the cost incurred by the policy and the optimal policy over some time horizon $T$. In particular we consider the Retro Renting (RR) and Follow The Perturbed Leader (FTPL) policies proposed in the literature and provide performance guarantees on the regret of these policies. We show that under i.i.d stochastic arrivals, RR policy has linear regret while FTPL policy has constant regret. Next, we propose a variant of FTPL, namely Wait then FTPL (W-FTPL), which also has constant regret while demonstrating much better dependence on the fetch cost. We also show that under adversarial arrivals, RR policy has linear regret while both FTPL and W-FTPL have regret $\mathrm{O}(\sqrt{T})$ which is order-optimal.

翻译：我们研究服务托管问题，其中服务提供商可通过短期合同动态租赁边缘资源，以提升客户服务质量。服务也可部分托管于边缘节点，此时客户的请求可在边缘侧获得部分处理。系统总成本由三部分组成：租赁成本、因服务客户延迟产生的服务成本、以及将服务的代码/数据库从云服务器获取至边缘节点托管所需的带宽造成的获取成本。本文以遗憾值为指标比较多种托管策略——遗憾值定义为策略成本与最优策略成本在时间范围$T$内的差值。我们特别考察了文献中提出的回溯租赁（RR）与跟随扰动领先者（FTPL）策略，并给出了这两种策略的遗憾值性能保证。研究表明：在独立同分布随机到达场景下，RR策略呈现线性遗憾值，而FTPL策略具有常数遗憾值。随后我们提出FTPL的变体——等待后FTPL（W-FTPL），该策略同样保持常数遗憾值，但对获取成本的依赖显著降低。我们还证明：在对抗性到达场景下，RR策略具有线性遗憾值，而FTPL与W-FTPL策略的遗憾值均为$\mathrm{O}(\sqrt{T})$，达到阶数最优。