基于稀疏加性信念模型的知识梯度策略
The Knowledge Gradient Policy Using A Sparse Additive Belief Model
AI总结：
本文提出一种用于高维稀疏信念函数的序贯学习策略，结合贝叶斯R&S与频率学学习，通过B-样条基扩展和非参数加性模型实现稀疏线性模型参数估计。
摘要：
我们提出了一种用于噪声离散全局优化和排序选择问题的序贯学习策略，其中高维稀疏信念函数包含数百甚至数千个特征，但仅有少量特征具有解释力。我们推导了带有组Lasso惩罚的稀疏线性模型的知识梯度策略（KGSpLin），该策略是贝叶斯R&S与频率学学习的混合方法。特别地，我们的方法自然结合了B-样条基扩展，并推广到非参数加性模型（KGSpAM）和函数ANOV模型。理论上，我们提供了后验均值估计和函数估计的误差界。受控实验表明，该算法即使在嵌入数百个虚参数的模型中也能高效学习正确非零参数集，并优于线性模型的知识梯度方法。
英文摘要：
We propose a sequential learning policy for noisy discrete global optimization and ranking and selection (R\&S) problems with high dimensional sparse belief functions, where there are hundreds or even thousands of features, but only a small portion of these features contain explanatory power. We aim to identify the sparsity pattern and select the best alternative before the finite budget is exhausted. We derive a knowledge gradient policy for sparse linear models (KGSpLin) with group Lasso penalty. This policy is a unique and novel hybrid of Bayesian R\&S with frequentist learning. Particularly, our method naturally combines B-spline basis expansion and generalizes to the nonparametric additive model (KGSpAM) and functional ANOVA model. Theoretically, we provide the estimation error bounds of the posterior mean estimate and the functional estimate. Controlled experiments show that the algorithm efficiently learns the correct set of nonzero parameters even when the model is imbedded with hundreds of dummy parameters. Also it outperforms the knowledge gradient for a linear model.
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