论文标题

递归专家:在动态环境中学习系统的有效最佳混合

Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments

论文作者

Gokcesu, Kaan, Gokcesu, Hakan

论文摘要

顺序学习系统用于从决策到优化的各种问题,它们为自然提供了“信念”(意见),然后根据反馈(结果)更新这种信念,以最大程度地减少(或最大化)一些成本或损失(相反,公用事业或收益)。目标是通过利用自然反馈(状态)固有的时间关系来实现目标。通过利用这种关系,可以设计特定的学习系统,该系统对各种应用程序均无无疑最佳。但是,如果问题的框架不是静止的,即自然状态有时任意变化,那么系统所做的过去累积信念修订可能会变得无用,并且如果缺乏适应性,系统可能会失败。虽然可以在特定情况下(例如凸优化)直接实现这种适应性,但对于一般学习任务而言,它主要不是直接的。为此,我们为一般顺序学习系统提出了一个有效的最佳混合框架,我们将其称为动态环境的递归专家。为此,我们设计了超专长,以使学习系统可以使用,并以特定的方式递归合并,以实现最小值的最佳遗憾,达到了恒定的因素。从初始系统到我们自适应系统的计算复杂性的乘法增加仅是对数的时间因素。

Sequential learning systems are used in a wide variety of problems from decision making to optimization, where they provide a 'belief' (opinion) to nature, and then update this belief based on the feedback (result) to minimize (or maximize) some cost or loss (conversely, utility or gain). The goal is to reach an objective by exploiting the temporal relation inherent to the nature's feedback (state). By exploiting this relation, specific learning systems can be designed that perform asymptotically optimal for various applications. However, if the framework of the problem is not stationary, i.e., the nature's state sometimes changes arbitrarily, the past cumulative belief revision done by the system may become useless and the system may fail if it lacks adaptivity. While this adaptivity can be directly implemented in specific cases (e.g., convex optimization), it is mostly not straightforward for general learning tasks. To this end, we propose an efficient optimal mixture framework for general sequential learning systems, which we call the recursive experts for dynamic environments. For this purpose, we design hyper-experts that incorporate the learning systems at our disposal and recursively merge in a specific way to achieve minimax optimal regret bounds up to constant factors. The multiplicative increases in computational complexity from the initial system to our adaptive system are only logarithmic-in-time factors.

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