In adaptive systems, predictors are used to anticipate changes in the systems state or behavior that may require system adaption, e.g., changing its configuration or adjusting resource allocation. Therefore, the quality of predictors is crucial for the overall reliability and performance of the system under control. This paper studies predictors in systems exhibiting probabilistic and non-deterministic behavior modelled as Markov decision processes (MDPs). Main contributions are the introduction of quantitative notions that measure the effectiveness of predictors in terms of their average capability to predict the occurrence of failures or other undesired system behaviors. The average is taken over all memoryless policies. We study two classes of such notions. One class is inspired by concepts that have been introduced in statistical analysis to explain the impact of features on the decisions of binary classifiers (such as precision, recall, f-score). Second, we study a measure that borrows ideas from recent work on probability-raising causality in MDPs and determines the quality of a predictor by the fraction of memoryless policies under which (the set of states in) the predictor is a probability-raising cause for the considered failure scenario.

翻译：在自适应系统中，预测器用于预判系统状态或行为中可能需要系统进行自适应调整的变化，例如改变其配置或调整资源分配。因此，预测器的质量对于受控系统的整体可靠性和性能至关重要。本文研究在呈现概率性和非确定性行为的系统中，被建模为马尔可夫决策过程（MDP）的预测器。主要贡献在于引入了定量概念，这些概念通过预测器预测故障或其他不良系统行为发生的平均能力来衡量其有效性。该平均值是在所有无记忆策略上计算的。我们研究了两类这样的概念。第一类概念受到统计学分析中为解释特征对二元分类器决策影响而引入的概念（如精确率、召回率、F值）的启发。其次，我们研究了一种度量方法，该方法借鉴了近期关于MDP中概率提升因果关系的研究成果，通过预测器（的状态集合）在多大比例的无记忆策略下成为所考虑故障场景的概率提升原因来确定预测器的质量。