The online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack. In this paper, we study a general version that includes item departures, while also considering multiple knapsacks and multi-dimensional item sizes. We design a threshold-based online algorithm and prove that the algorithm can achieve order-optimal competitive ratios. Beyond worst-case performance guarantees, we also aim to achieve near-optimal average performance under typical instances. Towards this goal, we propose a data-driven online algorithm that learns within a policy-class that guarantees a worst-case performance bound. In trace-driven experiments, we show that our data-driven algorithm outperforms other benchmark algorithms in an application of online knapsack to job scheduling for cloud computing.

翻译：在线背包问题是网络与运筹学中经典的在线资源分配问题。其基本版本研究如何将在线到达的不同大小与价值的物品装入容量有限的背包中。本文研究包含物品离开的通用版本，同时考虑多个背包及多维物品大小。我们设计了一种基于阈值的在线算法，并证明该算法可实现阶优的竞争比。除最坏情况性能保证外，我们还致力于在典型实例下实现接近最优的平均性能。为此，我们提出一种数据驱动的在线算法，该算法在保证最坏情况性能的策略类中进行学习。在基于轨迹驱动的实验中，我们展示了所提数据驱动算法在云计算作业调度这一在线背包应用场景中优于其他基准算法。