Meta-LinEXP3: Online-within-Online Learning for Adversarial Linear Contextual Bandits

2026-09-09

AI Summary

为了解决随机动作集对抗线性情境盗匪问题，提出Meta-LinEXP3算法，通过先前任务构建任务级先验以指导内层学习者，并在已知与未知分布情况下分别设计估计器来优化遗憾界。

Abstract

Meta-learning has emerged as an effective paradigm for transferring knowledge across sequential bandit tasks. While substantial progress has been made for stochastic bandits and non-contextual adversarial bandits, meta-learning for adversarial linear contextual bandits (ALCBs) with random action sets remains largely unexplored. To address this problem, we propose Meta-LinEXP3, an online-within-online algorithm that constructs a predictable task-level prior from completed tasks to guide the inner LinEXP3 learner. For known context distributions, we develop a policy-centered estimator that achieves an intrinsic-dimension $\mathcal{O}(\sqrt{n})$ per-task regret bound. For unknown distributions, we introduce a past-only regularized moment estimator with an $\mathcal{O}(n^{2/3})$ leading regret term and explicit finite-sample error. We further establish a direct connection between prior accuracy and transfer regret, showing that increasingly accurate priors yield sublinear transfer-dependent regret across tasks. Experiments demonstrate the effectiveness of Meta-LinEXP3, including its application to structured hyperspectral tensor sampling.

Problem

• Meta-learning
• Adversarial Linear Contextual Bandits
• Random Action Sets

Innovation

• Meta-LinEXP3
• adversarial linear contextual bandits
• online-within-online learning
• policy-centered estimator
• transfer regret