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Optimal Value of Information in Dynamic Bayesian Networks

机译：动态贝叶斯网络中信息的最优价值

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摘要

Decision-making based on probabilistic reasoning often involves selecting a subset of expensive observations, that best predict the system state. Krause and Guestrin described two problems of non-myopically selecting observations in graphical models to optimize the value of information (VoI), namely, selection of an optimal subset of observations, and generation of an optimal conditional observation plan. They showed that these problems are intractable in general, but gave polynomial-time dynamic programming algorithms, called VoIDP, for chain graphical models. In this paper, we consider the general setting of Dynamic Bayesian Networks (DBNs), and formulate these problems in terms of finding optimal policies in Markov Decision Processes (MDPs). The time complexities of the resulting algorithms are exponential in general, but polynomial for chain models. Given a chain model, our algorithms compute the same subset, or plan, as VoIDP. Interestingly, despite their generality, our algorithms have significantly better time complexities for chain models compared to VoIDP. We also present an outline of how to use our framework to formulate an approximate, nonmyopic VoI optimization technique, with absolute a posteriori guarantees on approximation, that can handle arbitrary DBNs efficiently.
机译：基于概率推理的决策通常涉及选择一组昂贵的观测值，这些观测值可以最佳地预测系统状态。 Krause和Guestrin描述了在图形模型中非近视选择观察以优化信息（VoI）值的两个问题，即选择观察的最佳子集和生成最佳条件观察计划。他们表明这些问题通常是棘手的，但是给出了用于链图形模型的多项式时间动态规划算法，称为VoIDP。在本文中，我们考虑了动态贝叶斯网络（DBN）的一般设置，并根据在马尔可夫决策过程（MDP）中寻找最佳策略来阐述这些问题。所得算法的时间复杂度通常是指数级的，但是对于链模型来说是多项式的。给定链模型，我们的算法将计算与VoIDP相同的子集或计划。有趣的是，尽管它们具有通用性，但与VoIDP相比，我们的算法在链模型上的时间复杂度要好得多。我们还概述了如何使用我们的框架来制定近似的，非近视的VoI优化技术，并在近似值上绝对具有后验保证，可以有效地处理任意DBN。

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