论文标题
部分可观测时空混沌系统的无模型预测
Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimization
论文作者
论文摘要
我们研究上下文搜索的问题，在对抗性噪声模型中，在更高维度中二进制搜索的概括。令$ d $为问题的维度，$ t $是时间范围，$ c $是系统中对抗噪声的总量。我们专注于$ε$ -BALL和绝对损失。对于$ε$ -BALL的损失，我们给出了$ O（C + D \ log（1/ε））$的紧密遗憾，改善了$ O（d^3 \ log（1/ε）\ log^2（t） + c \ log（t） + c \ log（t）\ log（1/ε））$ Krishnamurthy et al（Operative''23）。对于绝对损失，我们给出了一种有效的算法，并带有后悔的$ O（C+D \ log T）$。为了解决绝对损失案例，我们研究了具有独立感兴趣的亚级别反馈的腐败凸出优化的更一般环境。 我们的技术与先前的方法有很大的不同。具体而言，我们跟踪候选目标向量上的密度功能，而不是由候选目标向量组成的知识集，该求目标向量与获得的反馈一致。
We study the problem of contextual search, a generalization of binary search in higher dimensions, in the adversarial noise model. Let $d$ be the dimension of the problem, $T$ be the time horizon and $C$ be the total amount of adversarial noise in the system. We focus on the $ε$-ball and the absolute loss. For the $ε$-ball loss, we give a tight regret bound of $O(C + d \log(1/ε))$ improving over the $O(d^3 \log(1/ε) \log^2(T) + C \log(T) \log(1/ε))$ bound of Krishnamurthy et al (Operations Research '23). For the absolute loss, we give an efficient algorithm with regret $O(C+d \log T)$. To tackle the absolute loss case, we study the more general setting of Corruption-Robust Convex Optimization with Subgradient feedback, which is of independent interest. Our techniques are a significant departure from prior approaches. Specifically, we keep track of density functions over the candidate target vectors instead of a knowledge set consisting of the candidate target vectors consistent with the feedback obtained.
