论文标题
在Banach空间上的信息投影，并应用于国家独立kl加权最佳控制
Information Projection on Banach spaces with Applications to State Independent KL-Weighted Optimal Control
论文作者
论文摘要
本文研究了关于高斯参考度量的Banach空间上的信息预测。具体来说，我们的兴趣在于将参考度量的投影（相对于KL-Divergence）表征到对应于平均值变化（或{\ it Shift shipt措施}）的一组度量。作为我们的主要结果，我们给出了一个Portmanteau定理，该定理表征了该问题的几种不同配方之间的关系。在Banach空间上高斯措施的一般环境中，我们表明此信息投影问题等于最大程度地减少了与相关随机过程相对于某些Onsager-Machlup（OM）功能。然后，我们在更具体的经典Wiener空间设置中构建了一些重新策划。首先，我们表明，对于我们能够表征的相关随机过程，也可以根据OM函数来表达对KL加权优化。接下来，我们将通过构建适当的惩罚函数来展示如何通过明确的功能约束来编码可行的移动措施集。最后，我们将信息投影问题表示为变异问题的计算，该问题通过Euler-Lagrange方程提出了解决方案过程。我们为几个特定示例详细介绍了这些重新措施的细节。
This paper studies constrained information projections on Banach spaces with respect to a Gaussian reference measure. Specifically our interest lies in characterizing projections of the reference measure, with respect to the KL-divergence, onto sets of measures corresponding to changes in the mean (or {\it shift measures}). As our main result, we give a portmanteau theorem that characterizes the relationship among several different formulations of this problem. In the general setting of Gaussian measures on a Banach space, we show that this information projection problem is equivalent to minimization of a certain Onsager-Machlup (OM) function with respect to an associated stochastic process. We then construct several reformulations in the more specific setting of classical Wiener space. First, we show that KL-weighted optimization over shift measures can also be expressed in terms of an OM function for an associated stochastic process that we are able to characterize. Next, we show how to encode the feasible set of shift measures through an explicit functional constraint by constructing an appropriate penalty function. Finally, we express our information projection problem as a calculus of variations problem, which suggests a solution procedure via the Euler-Lagrange equation. We work out the details of these reformulations for several specific examples.
