Online Fractional Knapsack With Predictions

Mohammadreza Daneshvaramoli, Helia Karisani, Adam Lechowicz, Bo Sun, Cameron N Musco, Mohammad Hajiesmaili

Primary Area: optimization

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Keywords: online fractional knapsack, advice, learning-augmented algorithm, robustness, consistency

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Abstract:

The well-known classical version of the online knapsack problem decides which of the arriving items of different weights and values to accept into a capacity-limited knapsack. In this paper, we consider the online fractional knapsack problem where items can be fractionally accepted. We present the first online algorithms for this problem which incorporate prediction about the input in several forms, including predictions of the smallest value chosen in the optimal offline solution, and interval predictions which give upper and lower bounds on this smallest value.
We present algorithms for both of these prediction models, prove their competitive ratios, and give a matching worst-case lower bound. Furthermore, we present a learning-augmented meta-algorithm that combines our prediction techniques with a robust baseline algorithm to simultaneously achieve consistency and robustness.
Finally, we conduct numerical experiments that show that our prediction algorithms significantly outperform a simple greedy prediction algorithm for the problem and the robust baseline algorithm, which does not use predictions. Furthermore, we show that our learning-augmented algorithms can leverage imperfect predictions (e.g., from a machine learning model) to greatly improve average-case performance without sacrificing worst-case guarantees.

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Submission Number: 7769