arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.06705cs.LGstat.ML
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训练集上的优化泛化:一种同时训练参数和超参数的基于梯度的新框架

Optimizing generalization on the train set: a novel gradient-based framework to train parameters and hyperparameters simultaneously

Ecole Polytechnique(巴黎综合理工学院);Paris Dauphine-PSL(巴黎多芬大学-巴黎文理研究大学)

Karim Lounici, Katia Meziani, Benjamin Riu

摘要:

泛化是机器学习的核心问题。大多数预测方法都需要对保留的\textit{validation}数据集进行仔细的超参数校准,以实现泛化。本文的主要目标是提出一种新的方法,基于一种新的风险度量,使我们能够开发新的全自动程序的泛化。我们说明了这个新的框架在回归问题的相关性。这种新方法的主要优点是:(i)它可以同时训练模型,并在所有可用数据上的基于梯度的优化器的单次运行中执行正则化,而无需任何先前的超参数调整;(ii)这种框架可以同时处理几个额外的目标(相关性,稀疏性,.)$via$正则化参数的引入。值得注意的是,我们的方法转换超参数调整以及特征选择(组合离散优化问题)到一个连续的优化问题,这是通过经典的基于梯度的方法求解;(iii)我们的方法的计算复杂性是$O(npK)$其中$n,p,K$分别表示观测,功能和迭代的梯度下降算法的数量。我们在实验中观察到,与基准方法相比,我们的方法具有更小的运行时间,以获得相等的预测分数。我们的过程在PyTorch中实现(代码可用于复制)。

英文摘要:

Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is to present a novel approach based on a new measure of risk that allows us to develop novel fully automatic procedures for generalization. We illustrate the pertinence of this new framework in the regression problem. The main advantages of this new approach are: (i) it can simultaneously train the model and perform regularization in a single run of a gradient-based optimizer on all available data without any previous hyperparameter tuning; (ii) this framework can tackle several additional objectives simultaneously (correlation, sparsity,...) $via$ the introduction of regularization parameters. Noticeably, our approach transforms hyperparameter tuning as well as feature selection (a combinatorial discrete optimization problem) into a continuous optimization problem that is solvable via classical gradient-based methods ; (iii) the computational complexity of our methods is $O(npK)$ where $n,p,K$ denote respectively the number of observations, features and iterations of the gradient descent algorithm. We observe in our experiments a significantly smaller runtime for our methods as compared to benchmark methods for equivalent prediction score. Our procedures are implemented in PyTorch (code is available for replication).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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