We study learning to learn for regression problems through the lens of hyperparameter tuning. We propose the Langevin Gradient Descent Algorithm (LGD), which approximates the mean of the posterior distribution defined by the loss function and regularizer of a convex regression task. We prove the existence of an optimal hyperparameter configuration for which the LGD algorithm achieves the Bayes' optimal solution for squared loss. Subsequently, we study generalization guarantees on meta-learning optimal hyperparameters for the LGD algorithm from a given set of tasks in the data-driven setting. For a number of parameters $d$ and hyperparameter dimension $h$, we show a pseudo-dimension bound of $O(dh)$, upto logarithmic terms under mild assumptions on LGD. This matches the dimensional dependence of the bounds obtained in prior work for the elastic net, which only allows for $h=2$ hyperparameters, and extends their bounds to regression on convex loss. Finally, we show empirical evidence of the success of LGD and the meta-learning procedure for few-shot learning on linear regression using a few synthetically created datasets.

In this paper, we introduce and analyze Discriminative State-Space Models for forecasting non-stationary time series. We provide data-dependent generalization guarantees for learning these models based on the recently introduced notion of discrepancy. We provide an in-depth analysis of the complexity of such models. Finally, we also study the generalization guarantees for several structural risk minimization approaches to this problem and provide an efficient implementation for one of them which is based on a convex objective.

However, differential privacy's worst-case nature entails scaling such noise to the range of the queries even for

However, differential privacy's worst-case nature entails scaling such noise to the range of the queries even for

Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and the loss function used in a subsequent learning task, where the data generated by a GAN serves for training. Taking that structural information into account is also important to derive generalization guarantees. Thus, we propose to use the discrepancy measure, which was originally introduced for the closely related problem of domain adaptation and which precisely takes into account the hypothesis set and the loss function. We show that discrepancy admits favorable properties for training GANs and prove explicit generalization guarantees. We present efficient algorithms using discrepancy for two tasks: training a GAN directly, namely DGAN, and mixing previously trained generative models, namely EDGAN. Our experiments on toy examples and several benchmark datasets show that DGAN is competitive with other GANs and that EDGAN outperforms existing GAN ensembles, such as AdaGAN.