Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional regularization techniques are known to improve generalization when the data exhibits low-dimensional structure like sparsity. However, it is largely unexplored how to leverage this structure in the context of multi-objective learning (MOL) with multiple competing objectives. In this work, we discuss how the application of vanilla regularization approaches can fail, and propose a two-stage MOL framework that can successfully leverage low-dimensional structure. We demonstrate its effectiveness experimentally for multi-distribution learning and fairness-risk trade-offs.

Despite achieving promising fairness-error trade-offs, in-processing mitigation techniques for group fairness cannot be employed in numerous practical applications with limited computation resources or no access to the training pipeline of the prediction model. In these situations, post-processing is a viable alternative. However, current methods are tailored to specific problem settings and fairness definitions and hence, are not as broadly applicable as in-processing. In this work, we propose a framework that turns any regularized in-processing method into a post-processing approach. This procedure prescribes a way to obtain post-processing techniques for a much broader range of problem settings than the prior post-processing literature. We show theoretically and through extensive experiments that our framework preserves the good fairness-error trade-offs achieved with in-processing and can improve over the effectiveness of prior post-processing methods. Finally, we demonstrate several advantages of a modular mitigation strategy that disentangles the training of the prediction model from the fairness mitigation, including better performance on tasks with partial group labels.

It is widely believed that given the same labeling budget, active learning (AL) algorithms like margin-based active learning achieve better predictive performance than passive learning (PL), albeit at a higher computational cost. Recent empirical evidence suggests that this added cost might be in vain, as margin-based AL can sometimes perform even worse than PL. While existing works offer different explanations in the low-dimensional regime, this paper shows that the underlying mechanism is entirely different in high dimensions: we prove for logistic regression that PL outperforms margin-based AL even for noiseless data and when using the Bayes optimal decision boundary for sampling. Insights from our proof indicate that this high-dimensional phenomenon is exacerbated when the separation between the classes is small. We corroborate this intuition with experiments on 20 high-dimensional datasets spanning a diverse range of applications, from finance and histology to chemistry and computer vision.

Prior theoretical and empirical works have established that semi-supervised learning algorithms can leverage the unlabeled data to improve over the labeled sample complexity of supervised learning (SL) algorithms. However, existing theoretical work focuses on regimes where the unlabeled data is sufficient to learn a good decision boundary using unsupervised learning (UL) alone. This begs the question: Can SSL algorithms simultaneously improve upon both UL and SL? To this end, we derive a tight lower bound for 2-Gaussian mixture models that explicitly depends on the labeled and the unlabeled dataset size as well as the signal-to-noise ratio of the mixture distribution. Surprisingly, our result implies that no SSL algorithm improves upon the minimax-optimal statistical error rates of SL or UL algorithms for these distributions. Nevertheless, in our real-world experiments, SSL algorithms can often outperform UL and SL algorithms. In summary, our work suggests that while it is possible to prove the performance gains of SSL algorithms, this would require careful tracking of constants in the theoretical analysis.

Deep neural networks often predict samples with high confidence even when they come from unseen classes and should instead be flagged for expert evaluation. Current novelty detection algorithms cannot reliably identify such near OOD points unless they have access to labeled data that is similar to these novel samples. In this paper, we develop a new ensemble-based procedure for semi-supervised novelty detection (SSND) that successfully leverages a mixture of unlabeled ID and novel-class samples to achieve good detection performance. In particular, we show how to achieve disagreement only on OOD data using early stopping regularization. While we prove this fact for a simple data distribution, our extensive experiments suggest that it holds true for more complex scenarios: our approach significantly outperforms state-of-the-art SSND methods on standard image data sets (SVHN/CIFAR-10/CIFAR-100) and medical image data sets with only a negligible increase in computation cost.

Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge this narrative by showing that, even in the absence of noise, avoiding interpolation through ridge regularization can significantly improve generalization. We prove this phenomenon for the robust risk of both linear regression and classification, and hence provide the first theoretical result on \emph{robust overfitting}.