Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update

• URL: http://arxiv.org/abs/2507.11847v1
• Date: Wed, 16 Jul 2025 02:24:21 GMT
• Title: Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update
• Authors: Yu-Jie Zhang, Sheng-An Xu, Peng Zhao, Masashi Sugiyama,
• Abstract summary: We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function.<n>GLBs are widely applicable to real-world scenarios, but their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency.<n>We propose a jointly efficient algorithm that attains a nearly optimal regret bound with $mathcalO(1)$ time and space complexities per round.
• Score: 60.414548453838506
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function, thereby modeling a broad class of reward distributions such as Bernoulli and Poisson. While GLBs are widely applicable to real-world scenarios, their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency. Existing methods typically trade off between two objectives, either incurring high per-round costs for optimal regret guarantees or compromising statistical efficiency to enable constant-time updates. In this paper, we propose a jointly efficient algorithm that attains a nearly optimal regret bound with $\mathcal{O}(1)$ time and space complexities per round. The core of our method is a tight confidence set for the online mirror descent (OMD) estimator, which is derived through a novel analysis that leverages the notion of mix loss from online prediction. The analysis shows that our OMD estimator, even with its one-pass updates, achieves statistical efficiency comparable to maximum likelihood estimation, thereby leading to a jointly efficient optimistic method.

Related papers

• Distributionally Robust Optimization with Adversarial Data Contamination [36.409282287280185]
  We focus on optimizing Wasserstein-1 DRO objectives for generalized linear models with convex Lipschitz loss functions.<n>Our primary contribution lies in a novel modeling framework that integrates robustness against training data contamination with robustness against distributional shifts.<n>This work establishes the first rigorous guarantees, supported by efficient computation, for learning under the dual challenges of data contamination and distributional shifts.
  arXiv  Detail & Related papers  (2025-07-14T18:34:10Z)
• Self-Boost via Optimal Retraining: An Analysis via Approximate Message Passing [58.52119063742121]
  Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model performance.<n>This paper addresses the question of how to optimally combine the model's predictions and the provided labels.<n>Our main contribution is the derivation of the Bayes optimal aggregator function to combine the current model's predictions and the given labels.
  arXiv  Detail & Related papers  (2025-05-21T07:16:44Z)
• Provably Efficient Online RLHF with One-Pass Reward Modeling [59.30310692855397]
  We propose a one-pass reward modeling method that does not require storing the historical data and can be computed in constant time.<n>We provide theoretical guarantees showing that our method improves both statistical and computational efficiency.<n>We conduct experiments using Llama-3-8B-Instruct and Qwen2.5-7B-Instruct models on the Ultrafeedback-binarized and Mixture2 datasets.
  arXiv  Detail & Related papers  (2025-02-11T02:36:01Z)
• Achieving $\widetilde{\mathcal{O}}(\sqrt{T})$ Regret in Average-Reward POMDPs with Known Observation Models [56.92178753201331]
  We tackle average-reward infinite-horizon POMDPs with an unknown transition model.<n>We present a novel and simple estimator that overcomes this barrier.
  arXiv  Detail & Related papers  (2025-01-30T22:29:41Z)
• Adaptive debiased SGD in high-dimensional GLMs with streaming data [4.704144189806667]
  This paper introduces a novel approach to online inference in high-dimensional generalized linear models.<n>Our method operates in a single-pass mode, making it different from existing methods that require full dataset access or large-dimensional summary statistics storage.<n>The core of our methodological innovation lies in an adaptive descent algorithm tailored for dynamic objective functions, coupled with a novel online debiasing procedure.
  arXiv  Detail & Related papers  (2024-05-28T15:36:48Z)
• Federated Coordinate Descent for Privacy-Preserving Multiparty Linear Regression [0.5049057348282932]
  We present Federated Coordinate Descent, a new distributed scheme called FCD, to address this issue securely under multiparty scenarios. Specifically, through secure aggregation and added perturbations, our scheme guarantees that: (1) no local information is leaked to other parties, and (2) global model parameters are not exposed to cloud servers. We show that the FCD scheme fills the gap of multiparty secure Coordinate Descent methods and is applicable for general linear regressions, including linear, ridge and lasso regressions.
  arXiv  Detail & Related papers  (2022-09-16T03:53:46Z)
• Distributed Dynamic Safe Screening Algorithms for Sparse Regularization [73.85961005970222]
  We propose a new distributed dynamic safe screening (DDSS) method for sparsity regularized models and apply it on shared-memory and distributed-memory architecture respectively. We prove that the proposed method achieves the linear convergence rate with lower overall complexity and can eliminate almost all the inactive features in a finite number of iterations almost surely.
  arXiv  Detail & Related papers  (2022-04-23T02:45:55Z)
• Scalable Personalised Item Ranking through Parametric Density Estimation [53.44830012414444]
  Learning from implicit feedback is challenging because of the difficult nature of the one-class problem. Most conventional methods use a pairwise ranking approach and negative samplers to cope with the one-class problem. We propose a learning-to-rank approach, which achieves convergence speed comparable to the pointwise counterpart.
  arXiv  Detail & Related papers  (2021-05-11T03:38:16Z)
• Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination [29.85468294601847]
  We revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits. We show that our algorithms succeed where conventional methods fail.
  arXiv  Detail & Related papers  (2020-10-08T17:59:05Z)

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.