The Approximation Ratio for the Risk of Myopic Bayesian Active Learning for Linear Regression

• URL: http://arxiv.org/abs/2607.06642v1
• Date: Tue, 07 Jul 2026 15:07:41 GMT
• Title: The Approximation Ratio for the Risk of Myopic Bayesian Active Learning for Linear Regression
• Abstract summary: We prove a first-of-its-kind approximation ratio for the greedy algorithm's risk that is tight up to an absolute constant.<n>We illustrate the results with simple numerical simulations.
• Score: 1.2382630144282716
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Active learning studies the fundamental question: what data should we choose to observe? The greedy algorithm in optimal experiment design is a common heuristic and also equivalent to myopic Bayesian active learning for linear regression, the common framework where long-term planning is replaced with the one-step optimal choice. In this work, we prove a first-of-its-kind approximation ratio for the greedy algorithm's risk that is tight up to an absolute constant. The approximation ratio is linear in the maximum initial leverage score (MILS), a newly identified quantity fundamental to the greedy algorithm's performance. Finally, we illustrate the results with simple numerical simulations.

Related papers

• Asymptotically Optimal Linear Best Feasible Arm Identification with Fixed Budget [55.938644481736446]
  We introduce a novel algorithm for best feasible arm identification that guarantees an exponential decay in the error probability.<n>We validate our algorithm through comprehensive empirical evaluations across various problem instances with different levels of complexity.
  arXiv  Detail & Related papers  (2025-06-03T02:56:26Z)
• OKRidge: Scalable Optimal k-Sparse Ridge Regression [21.17964202317435]
  We propose a fast algorithm, OKRidge, for sparse ridge regression. We also propose a method to warm-start our solver, which leverages a beam search.
  arXiv  Detail & Related papers  (2023-04-13T17:34:44Z)
• Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
  Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
  arXiv  Detail & Related papers  (2023-04-12T14:51:47Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Efficient and Near-Optimal Smoothed Online Learning for Generalized Linear Functions [28.30744223973527]
  We give a computationally efficient algorithm that is the first to enjoy the statistically optimal log(T/sigma) regret for realizable K-wise linear classification. We develop a novel characterization of the geometry of the disagreement region induced by generalized linear classifiers.
  arXiv  Detail & Related papers  (2022-05-25T21:31:36Z)
• Sparse Bayesian Learning via Stepwise Regression [1.2691047660244335]
  We propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) As its noise variance parameter goes to zero, RMP exhibits a surprising connection to Stepwise Regression. We derive novel guarantees for Stepwise Regression algorithms, which also shed light on RMP.
  arXiv  Detail & Related papers  (2021-06-11T00:20:27Z)
• An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits [129.1029690825929]
  We introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We establish minimax optimality for any learning horizon in the special case of non-contextual linear bandits.
  arXiv  Detail & Related papers  (2020-10-23T09:12:47Z)
• A spectral algorithm for robust regression with subgaussian rates [0.0]
  We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples. The goal is to design a procedure which attains the optimal sub-gaussian error bound even though the data have only finite moments.
  arXiv  Detail & Related papers  (2020-07-12T19:33:50Z)
• Fast OSCAR and OWL Regression via Safe Screening Rules [97.28167655721766]
  Ordered $L_1$ (OWL) regularized regression is a new regression analysis for high-dimensional sparse learning. Proximal gradient methods are used as standard approaches to solve OWL regression. We propose the first safe screening rule for OWL regression by exploring the order of the primal solution with the unknown order structure.
  arXiv  Detail & Related papers  (2020-06-29T23:35:53Z)
• Meta-learning with Stochastic Linear Bandits [120.43000970418939]
  We consider a class of bandit algorithms that implement a regularized version of the well-known OFUL algorithm, where the regularization is a square euclidean distance to a bias vector. We show both theoretically and experimentally, that when the number of tasks grows and the variance of the task-distribution is small, our strategies have a significant advantage over learning the tasks in isolation.
  arXiv  Detail & Related papers  (2020-05-18T08:41:39Z)

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.