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

• URL: http://arxiv.org/abs/2603.18157v1
• Date: Wed, 18 Mar 2026 18:00:34 GMT
• Title: Learning-Augmented Algorithms for $k$-median via Online Learning
• Abstract summary: We introduce a novel model for learning-augmented algorithms inspired by online learning.<n>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.
• Score: 16.98221371037775
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• A Survey of Meta-features Used for Automated Selection of Algorithms for Black-box Single-objective Continuous Optimization [4.173197621837912]
  We conduct an overview of the key contributions to algorithm selection in the field of single-objective continuous black-box optimization. We study machine learning models for automated algorithm selection, configuration, and performance prediction.
  arXiv  Detail & Related papers  (2024-06-08T11:11:14Z)
• Large Language Model-Enhanced Algorithm Selection: Towards Comprehensive Algorithm Representation [27.378185644892984]
  This paper introduces Large Language Models (LLMs) into algorithm selection for the first time. LLMs not only captures the structural and semantic aspects of the algorithm, but also demonstrates contextual awareness and library function understanding. The selected algorithm is determined by the matching degree between a given problem and different algorithms.
  arXiv  Detail & Related papers  (2023-11-22T06:23:18Z)
• Neural Algorithmic Reasoning Without Intermediate Supervision [21.852775399735005]
  We focus on learning neural algorithmic reasoning only from the input-output pairs without appealing to the intermediate supervision. We build a self-supervised objective that can regularise intermediate computations of the model without access to the algorithm trajectory. We demonstrate that our approach is competitive to its trajectory-supervised counterpart on tasks from the CLRSic Algorithmic Reasoning Benchmark.
  arXiv  Detail & Related papers  (2023-06-23T09:57:44Z)
• Dual Algorithmic Reasoning [9.701208207491879]
  We propose to learn algorithms by exploiting duality of the underlying algorithmic problem. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task.
  arXiv  Detail & Related papers  (2023-02-09T08:46:23Z)
• Improved Algorithms for Neural Active Learning [74.89097665112621]
  We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. We introduce two regret metrics by minimizing the population loss that are more suitable in active learning than the one used in state-of-the-art (SOTA) related work.
  arXiv  Detail & Related papers  (2022-10-02T05:03:38Z)
• Machine Learning for Online Algorithm Selection under Censored Feedback [71.6879432974126]
  In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. We adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon.
  arXiv  Detail & Related papers  (2021-09-13T18:10:52Z)
• Algorithm Selection on a Meta Level [58.720142291102135]
  We introduce the problem of meta algorithm selection, which essentially asks for the best way to combine a given set of algorithm selectors. We present a general methodological framework for meta algorithm selection as well as several concrete learning methods as instantiations of this framework.
  arXiv  Detail & Related papers  (2021-07-20T11:23:21Z)
• Benchmarking Simulation-Based Inference [5.3898004059026325]
  Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency.
  arXiv  Detail & Related papers  (2021-01-12T18:31:22Z)
• Evolving Reinforcement Learning Algorithms [186.62294652057062]
  We propose a method for meta-learning reinforcement learning algorithms. The learned algorithms are domain-agnostic and can generalize to new environments not seen during training. We highlight two learned algorithms which obtain good generalization performance over other classical control tasks, gridworld type tasks, and Atari games.
  arXiv  Detail & Related papers  (2021-01-08T18:55:07Z)
• Run2Survive: A Decision-theoretic Approach to Algorithm Selection based on Survival Analysis [75.64261155172856]
  survival analysis (SA) naturally supports censored data and offers appropriate ways to use such data for learning distributional models of algorithm runtime. We leverage such models as a basis of a sophisticated decision-theoretic approach to algorithm selection, which we dub Run2Survive. In an extensive experimental study with the standard benchmark ASlib, our approach is shown to be highly competitive and in many cases even superior to state-of-the-art AS approaches.
  arXiv  Detail & Related papers  (2020-07-06T15:20:17Z)
• Extreme Algorithm Selection With Dyadic Feature Representation [78.13985819417974]
  We propose the setting of extreme algorithm selection (XAS) where we consider fixed sets of thousands of candidate algorithms. We assess the applicability of state-of-the-art AS techniques to the XAS setting and propose approaches leveraging a dyadic feature representation.
  arXiv  Detail & Related papers  (2020-01-29T09:40:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.