提出SCaLE算法，解决在线优化中切换成本过高的问题。
SCaLE: Switching Cost aware Learning and Exploration
- 设计新算法SCaLE，自动适应动态代价变化
- 实现无分布假设下的亚线性动态后悔，无需代价结构先验
- 适合高维动态优化场景，如在线学习与控制
本文针对带宽在线凸优化中的无界度量移动成本问题，考虑高维动态二次损失代价与ℓ₂范数切换代价，在噪声带宽反馈模型下展开研究。对于一类通用随机环境，首次提出算法SCaLE，可在未知损失代价结构的情况下，保证分布无关的亚线性动态后悔。研究过程中提出一种新颖的谱后悔分析方法，分别量化了特征值误差驱动的后悔与特征基扰动驱动的后悔。大量数值实验对比现有在线学习基线，验证了算法有效性，并展示了其统计一致性。
原文摘要 · Abstract (English)
This work addresses the fundamental problem of unbounded metric movement costs in bandit online convex optimization, by considering high-dimensional dynamic quadratic hitting costs and $\ell_2$-norm switching costs in a noisy bandit feedback model. For a general class of stochastic environments, we provide the first algorithm SCaLE that provably achieves a distribution-agnostic sub-linear dynamic regret, without the knowledge of hitting cost structure. En-route, we present a novel spectral regret analysis that separately quantifies eigenvalue-error driven regret and eigenbasis-perturbation driven regret. Extensive numerical experiments, against online-learning baselines, corroborate our claims, and highlight statistical consistency of our algorithm.
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