Decision-Theoretic Approaches for Improved Learning-Augmented Algorithms

TL;DR

This paper develops decision-theoretic metrics to evaluate and improve learning-augmented algorithms, enabling better performance trade-offs and comparisons across algorithms using deterministic and stochastic measures.

Contribution

It introduces a systematic framework using decision-theoretic metrics for analyzing algorithms with learned predictions, applicable to various online decision problems.

Findings

Framework quantifies algorithm performance across prediction errors

Balances performance and risk in algorithm design

Applied to ski-rental, one-max search, and contract scheduling

Abstract

We initiate the systematic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that help us quantify how close the algorithm is to an ideal solution, and stochastic measures that balance the trade-off between the algorithm's performance and the risk associated with the imperfect oracle. These approaches allow us to quantify the algorithm's performance across the full spectrum of the prediction error, and thus choose the best algorithm within an entire class of otherwise incomparable ones. We apply our framework to three well-known problems from online decision making, namely ski-rental, one-max search, and contract scheduling.