Pareto-Optimality, Smoothness, and Stochasticity in Learning-Augmented One-Max-Search

TL;DR

This paper introduces a novel learning-augmented algorithm for the One-Max search problem that optimally balances consistency and robustness, and extends analysis to stochastic settings with randomness in prices and predictions.

Contribution

It presents the first algorithm achieving both smoothness and optimal worst-case guarantees in learning-augmented One-Max search.

Findings

The algorithm attains the best trade-off between consistency and robustness.

It extends analysis to stochastic settings with randomness in prices and predictions.

Provides theoretical guarantees in both adversarial and stochastic scenarios.

Abstract

One-max search is a classic problem in online decision-making, in which a trader acts on a sequence of revealed prices and accepts one of them irrevocably to maximise its profit. The problem has been studied both in probabilistic and in worst-case settings, notably through competitive analysis, and more recently in learning-augmented settings in which the trader has access to a prediction on the sequence. However, existing approaches either lack smoothness, or do not achieve optimal worst-case guarantees: they do not attain the best possible trade-off between the consistency and the robustness of the algorithm. We close this gap by presenting the first algorithm that simultaneously achieves both of these important objectives. Furthermore, we show how to leverage the obtained smoothness to provide an analysis of one-max search in stochastic learning-augmented settings which capture randomness in both the observed prices and the prediction.