In the online knapsack problem, the goal is to pack items arriving online with different values and weights into a capacity-limited knapsack to maximize the total value of the accepted items. We study \textit{learning-augmented} algorithms for this problem, which aim to use machine-learned predictions to move beyond pessimistic worst-case guarantees. Existing learning-augmented algorithms for online knapsack consider relatively complicated prediction models that give an algorithm substantial information about the input, such as the total weight of items at each value. In practice, such predictions can be error-sensitive and difficult to learn. Motivated by this limitation, we introduce a family of learning-augmented algorithms for online knapsack that use \emph{succinct predictions}. In particular, the machine-learned prediction given to the algorithm is just a single value or interval that estimates the minimum value of any item accepted by an offline optimal solution. By leveraging a relaxation to online \emph{fractional} knapsack, we design algorithms that can leverage such succinct predictions in both the trusted setting (i.e., with perfect prediction) and the untrusted setting, where we prove that a simple meta-algorithm achieves a nearly optimal consistency-robustness trade-off. Empirically, we show that our algorithms significantly outperform baselines that do not use predictions and often outperform algorithms based on more complex prediction models.

翻译：在线背包问题中，目标是将在线到达的具有不同价值和重量的物品装入容量有限的背包，以最大化所接受物品的总价值。我们研究了该问题的学习增强算法，这类算法旨在利用机器学习预测来突破悲观的最坏情况保证界限。现有的在线背包问题学习增强算法通常考虑相对复杂的预测模型，这些模型为算法提供了关于输入的大量信息，例如每个价值层级下物品的总重量。在实践中，此类预测可能对误差敏感且难以学习。受此局限性的启发，我们引入了一类基于简洁预测的在线背包问题学习增强算法。具体而言，提供给算法的机器学习预测仅为一个单一数值或区间，用于估计离线最优解所接受的任何物品的最小价值。通过松弛到在线分数背包问题，我们设计了能够在可信设置（即预测完美）和不可信设置中利用此类简洁预测的算法。在不可信设置中，我们证明一个简单的元算法能够实现近乎最优的一致性-鲁棒性权衡。实证研究表明，我们的算法显著优于不使用预测的基线方法，并且通常优于基于更复杂预测模型的算法。