提出统一正则化方法，解决高维张量强化学习难题
A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits
- 用凸优化与可分解正则化建模张量低秩结构
- 理论证明比现有方法更优且适用范围更广
- 适合处理高维复杂上下文的决策问题
现代决策场景常面临高维且富含高阶上下文信息的数据，现有强化学习算法难以生成有效策略。本文提出一种广义线性张量强化学习算法，通过引入低维张量结构，并建立统一的分析框架。该框架采用弱可分解正则化与凸优化方法，不仅在张量低秩假设下表现更优，还可扩展至切片稀疏性、低秩等多种低维结构。理论分析表明，相比已有低秩张量结果，本框架不仅提供更紧的泛化误差界，且适用性更广。在退化为低秩矩阵的特殊情形下，其边界在某些场景仍具优势。
原文摘要 · Abstract (English)
Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper a generalized linear tensor bandits algorithm designed to tackle these challenges by incorporating low-dimensional tensor structures, and further derive a unified analytical framework of the proposed algorithm. Specifically, our framework introduces a convex optimization approach with the weakly decomposable regularizers, enabling it to not only achieve better results based on the tensor low-rankness structure assumption but also extend to cases involving other low-dimensional structures such as slice sparsity and low-rankness. The theoretical analysis shows that, compared to existing low-rankness tensor result, our framework not only provides better bounds but also has a broader applicability. Notably, in the special case of degenerating to low-rank matrices, our bounds still offer advantages in certain scenarios.
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