Learning-Augmented Algorithms for $k$-median via Online Learning

2026-03-18

AI Summary

This work addresses the challenge of improving the efficiency and performance of solving future $k$-median problem instances by leveraging historical data. It proposes the first learning-augmented framework that integrates online learning with approximation algorithms, adaptively generating high-quality clustering solutions from a sequence of dynamically changing instances to minimize the average approximation ratio. Theoretical analysis shows that the method’s average performance asymptotically approaches that of the best fixed solution in hindsight. Empirical evaluations demonstrate that the approach significantly outperforms baseline methods on both real-world and dynamic datasets while exhibiting strong adaptability. This study pioneers the incorporation of online learning into the design of learning-augmented clustering algorithms, offering a novel paradigm for dynamic optimization problems.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

The field of learning-augmented algorithms seeks to use ML techniques on past instances of a problem to inform an algorithm designed for a future instance. In this paper, we introduce a novel model for learning-augmented algorithms inspired by online learning. In this model, we are given a sequence of instances of a problem and the goal of the learning-augmented algorithm is to use prior instances to propose a solution to a future instance of the problem. The performance of the algorithm is measured by its average performance across all the instances, where the performance on a single instance is the ratio between the cost of the algorithm's solution and that of an optimal solution for that instance. We apply this framework to the classic $k$-median clustering problem, and give an efficient learning algorithm that can approximately match the average performance of the best fixed $k$-median solution in hindsight across all the instances. We also experimentally evaluate our algorithm and show that its empirical performance is close to optimal, and also that it automatically adapts the solution to a dynamically changing sequence.

Problem

• learning-augmented algorithms
• k-median
• online learning
• dynamic instances
• average performance

Innovation

• learning-augmented algorithms
• online learning
• k-median clustering
• dynamic adaptation
• average performance guarantee