具有边信息和无界损失函数的决策
Decision Making with Side Information and Unbounded Loss Functions
摘要：
研究了具有边信息和无界损失函数的决策问题。受可能近似正确的学习模型的启发，我们使用了一个稍微不同的模型，该模型以更通用的形式引入了边信息的概念，使其适用于更广泛的应用，包括参数估计和系统辨识。我们解决一致的决策与指数收敛行为的充分条件。在这方面，除了对损失函数类的增长函数有一定的条件外，损失函数类由一个可测函数支配就足够了，该可测函数的指数Orlicz期望在概率模型上是一致有界的。衰减指数，衰减常数，和样本的复杂性进行了讨论。实例应用的矩量法，最大似然估计，和系统辨识，以及说明。
英文摘要：
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in a more generic form to make it applicable to a broader class of applications including parameter estimation and system identification. We address sufficient conditions for consistent decision-making with exponential convergence behavior. In this regard, besides a certain condition on the growth function of the class of loss functions, it suffices that the class of loss functions be dominated by a measurable function whose exponential Orlicz expectation is uniformly bounded over the probabilistic model. Decay exponent, decay constant, and sample complexity are discussed. Example applications to method of moments, maximum likelihood estimation, and system identification are illustrated, as well.
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