List Update with Prediction

List Update is a fundamental problem in online algorithms, with a well-known 2-competitive algorithm that moves every requested element to the front. Randomization can slightly improve the competitive ratio to 1.6, but not beyond 1.5. However, practical inputs are not adversarial and one hopes to do better, particularly when additional information from a machine learning oracle is available. With access to predictions, the goal is to incur only a slight overhead compared to the prediction's accuracy, avoiding significant costs in case of substantial deviation.

We propose a (1+epsilon)-smooth randomized algorithm, offering robustness of O(1/epsilon^4). This guarantees that the algorithm never exceeds a cost greater than 1+epsilon times the prediction cost, while maintaining a bound within O(1/epsilon^4) of the optimal cost for every possible sequence. In cases where no paid swaps are permitted for the prediction, we can improve robustness to O(1/epsilon^2) while retaining 1+epsilon smoothness. We complement these findings by demonstrating a lower bound of 1/epsilon on the robustness for deterministic algorithms and log(1/epsilon) for randomized ones. Finally, the experiments we have made show that our algorithms perform better than the standard competitive algorithms for this problem