The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. Inspired by recent attention to fairness in online settings, we develop a natural and practically-relevant notion of time fairness for the online knapsack problem, and show that the existing optimal algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness and competitiveness. We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in practice, using trace-driven experiments. To further improve the trade-off between fairness and competitiveness, we develop a fair, robust (competitive), and consistent learning-augmented algorithm with substantial performance improvement in trace-driven experiments.

翻译：在线背包问题是在线算法领域的一个经典问题。其典型版本要求：如何在容量有限的背包中，对在线到达且具有不同价值和重量的物品进行打包，以最大化被接纳物品的总价值。尽管已知该问题存在最优竞争比算法，但这些算法可能在根本上缺乏公平性，即不同物品可能以多种方式受到不公平对待。受近期在线设置中公平性研究的启发，我们为在线背包问题定义了一种自然且具有实际意义的时间公平性概念，并证明现有最优算法在该指标下表现不佳。我们提出了一种参数化确定性算法，该参数精确刻画了公平性与竞争性之间的帕累托最优权衡。基于轨迹驱动的实验表明，理论上随机化具有足够的能力同时实现竞争性和公平性，然而在实践中表现不佳。为了进一步提升公平性与竞争性之间的权衡，我们开发了一种公平、鲁棒（具有竞争性）且一致的、基于学习增强的算法，在轨迹驱动实验中实现了显著的性能提升。