Meta-LinEXP3：对抗性线性上下文赌博机的在线内在线学习

中文摘要 AI 辅助

元学习已成为跨序列赌博机任务传递知识的有效范式。尽管在随机赌博机和非上下文对抗性赌博机方面已取得重大进展，但针对具有随机动作集的对抗性线性上下文赌博机（ALCBs）的元学习仍 largely 未被探索。为解决此问题，我们提出 Meta-LinEXP3，一种在线内在线算法，该算法从已完成任务中构建可预测的任务级先验，以指导内部 LinEXP3 学习器。对于已知上下文分布，我们开发了一种以策略为中心的估计器，实现了内在维度 $\nmathcal{O}(\sqrt{n})$ 的每任务遗憾界。对于未知分布，我们引入了一种仅使用过去数据的正则化矩估计器，其主导遗憾项为 $\mathcal{O}(n^{2/3})$，并具有明确的有限样本误差。我们进一步建立了先验准确性与迁移遗憾之间的直接联系，表明越来越准确的先验可跨任务产生次线性的迁移相关遗憾。实验证明了 Meta-LinEXP3 的有效性，包括其在结构化高光谱张量采样中的应用。

英文摘要

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.

发表机构

• College of Science, National University of Defense Technology（国防科技大学理学院）

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