We propose a new \emph{Transformed Risk Minimization} (TRM) framework as an extension of classical risk minimization. In TRM, we optimize not only over predictive models, but also over data transformations; specifically over distributions thereof. As a key application, we focus on learning augmentations; for instance appropriate rotations of images, to improve classification performance with a given class of predictors. Our TRM method (1) jointly learns transformations and models in a \emph{single training loop}, (2) works with any training algorithm applicable to standard risk minimization, and (3) handles any transforms, such as discrete and continuous classes of augmentations. To avoid overfitting when implementing empirical transformed risk minimization, we propose a novel regularizer based on PAC-Bayes theory. For learning augmentations of images, we propose a new parametrization of the space of augmentations via a stochastic composition of blocks of geometric transforms. This leads to the new \emph{Stochastic Compositional Augmentation Learning} (SCALE) algorithm. The performance of TRM with SCALE compares favorably to prior methods on CIFAR10/100. Additionally, we show empirically that SCALE can correctly learn certain symmetries in the data distribution (recovering rotations on rotated MNIST) and can also improve calibration of the learned model.

翻译：我们提出了一种新的变换风险最小化（TRM）框架，作为经典风险最小化的扩展。在TRM中，我们不仅优化预测模型，还优化数据变换，具体而言是变换的概率分布。作为关键应用，我们专注于学习增广策略，例如图像的适当旋转，以提升给定预测器类别的分类性能。我们的TRM方法能够（1）在单一训练循环中联合学习变换与模型，（2）适用于任何可用于标准风险最小化的训练算法，以及（3）处理任意变换，包括离散和连续类别的增广。为避免在实现经验化变换风险最小化时发生过拟合，我们基于PAC-Bayes理论提出了一种新颖的正则化项。针对图像增广学习，我们提出了一种通过几何变换块的随机组合来参数化增广空间的新方法，由此得到新颖的随机组合式增广学习（SCALE）算法。在CIFAR10/100数据集上，结合SCALE的TRM方法性能优于先前方法。此外，实验表明SCALE能正确学习数据分布中的某些对称性（在旋转MNIST中恢复出旋转模式），并改善学习模型的校准性能。