The problem of learning the parameters of a neural network is two-fold. First, we want that their training on a set of data via minimization of a suitable loss function succeed in finding a set of parameters for which the value of the loss is close to its global minimum.

In this paper, we study the generalization properties of Model-Agnostic MetaLearning (MAML) algorithms for supervised learning problems.

Determinantal point processes (DPPs) are random configurations of points with tunable negative dependence. Because sampling is tractable, DPPs are natural candidates for subsampling tasks, such as minibatch selection or coreset construction. A \emph{coreset} is a subset of a (large) training set, such that minimizing an empirical loss averaged over the coreset is a controlled replacement for the intractable minimization of the original empirical loss.Typically, the control takes the form of a guarantee that the average loss over the coreset approximates the total loss uniformly across the parameter space.Recent work has provided significant empirical support in favor of using DPPs to build randomized coresets, coupled with interesting theoretical results that are suggestive but leave some key questions unanswered.In particular, the central question of whether the cardinality of a DPP-based coreset is fundamentally smaller than one based on independent sampling remained open.In this paper, we answer this question in the affirmative, demonstrating that \emph{DPPs can provably outperform independently drawn coresets}. In this vein, we contribute a conceptual understanding of coreset loss as a \emph{linear statistic} of the (random) coreset. We leverage this structural observation to connect the coresets problem to a more general problem of concentration phenomena for linear statistics of DPPs, wherein we obtain \emph{effective concentration inequalities that extend well-beyond the state-of-the-art}, encompassing general non-projection, even non-symmetric kernels. The latter have been recently shown to be of interest in machine learning beyond coresets, but come with a limited theoretical toolbox, to the extension of which our result contributes. Finally, we are also able to address the coresets problem for vector-valued objective functions, a novelty in the coresets literature.

The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the rank-based loss is prevalent, replacing the empirical loss in many cases. The rank-based loss comprises a weighted sum of sorted individual losses, encompassing both convex losses like the spectral risk, which includes the empirical risk and conditional value-at-risk, and nonconvex losses such as the human-aligned risk and the sum of the ranked range loss. In this paper, we introduce a unified framework for the optimization of the rank-based loss through the utilization of a proximal alternating direction method of multipliers. We demonstrate the convergence and convergence rate of the proposed algorithm under mild conditions. Experiments conducted on synthetic and real datasets illustrate the effectiveness and efficiency of the proposed algorithm.

We study acceleration for distributed sparse regression in {\it high-dimensions}, which allows the parameter size to exceed and grow faster than the sample size. When applicable, existing distributed algorithms employing acceleration perform poorly in this setting, theoretically and numerically. We propose a new accelerated distributed algorithm suitable for high-dimensions. The method couples a suitable instance of accelerated Nesterov's proximal gradient with consensus and gradient-tracking mechanisms, aiming at estimating locally the gradient of the empirical loss while enforcing agreement on the local estimates. Under standard assumptions on the statistical model and tuning parameters, the proposed method is proved to globally converge at {\it linear} rate to an estimate that is within the {\it statistical precision} of the model. The iteration complexity scales as $\mathcal{O}(\sqrt{\kappa})$, while the communications per iteration are at most $\widetilde{\mathcal{O}}(\log m/(1-\rho))$, where $\kappa$ is the restricted condition number of the empirical loss, $m$ is the number of agents, and $\rho\in (0,1)$ measures the network connectivity. As by-product of our design, we also report an accelerated method for high-dimensional estimations over master-worker architectures, which is of independent interest and compares favorably with existing works.

Recent years have witnessed the rapid development of meta-learning in improving the meta generalization over tasks in few-shot learning. However, the task-specific level generalization is overlooked in most algorithms. For a novel few-shot learning task where the empirical distribution likely deviates from the true distribution, the model obtained via minimizing the empirical loss can hardly generalize to unseen data. A viable solution to improving the generalization comes as a more accurate approximation of the true distribution; that is, admitting a Gaussian-like vicinal distribution for each of the limited training samples. Thereupon we derive the resulting vicinal loss function over vicinities of all training samples and minimize it instead of the conventional empirical loss over training samples only, favorably free from the exhaustive sampling of all vicinal samples.It remains challenging to obtain the statistical parameters of the vicinal distribution for each sample. To tackle this challenge, we further propose to estimate the statistical parameters as the weighted mean and variance of a set of unlabeled data it passed by a random walk starting from training samples. To verify the performance of the proposed method, we conduct experiments on four standard few-shot learning benchmarks and consolidate the superiority of the proposed method over state-of-the-art few-shot learning baselines.