约束变化的在线预测问题的松弛层次
Hierarchies of Relaxations for Online Prediction Problems with Evolving Constraints
摘要：
我们研究在线预测的算法的遗憾是衡量通过不断发展的约束定义的基准。这个框架捕获了图上的在线预测，以及其他具有组合结构的预测问题。这里的一个关键方面是，由于约束的组合性质，找到最佳基准预测器（即使在事后，给定所有数据）可能在计算上很难。尽管如此，我们提供多项式时间\emph{prediction}算法，实现低遗憾对组合基准集。我们通过基于两个共同工作的想法构建不适当的学习算法来做到这一点。第一种是通过随机播放来减轻部分计算负担，第二种是采用Lasserre半定层次来近似得到的整数规划。有趣的是，对于我们的预测算法，我们只需要计算半定规划的值，而不是四舍五入的解。然而，Lasserre层次\emph{does}的完整性差距进入通用遗憾界的Rademacher复杂性的基准集。这在算法的计算时间和遗憾界之间建立了一个折衷。
英文摘要：
We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial structure. A key aspect here is that finding the optimal benchmark predictor (even in hindsight, given all the data) might be computationally hard due to the combinatorial nature of the constraints. Despite this, we provide polynomial-time \emph{prediction} algorithms that achieve low regret against combinatorial benchmark sets. We do so by building improper learning algorithms based on two ideas that work together. The first is to alleviate part of the computational burden through random playout, and the second is to employ Lasserre semidefinite hierarchies to approximate the resulting integer program. Interestingly, for our prediction algorithms, we only need to compute the values of the semidefinite programs and not the rounded solutions. However, the integrality gap for Lasserre hierarchy \emph{does} enter the generic regret bound in terms of Rademacher complexity of the benchmark set. This establishes a trade-off between the computation time and the regret bound of the algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
