Robust Regression of General ReLUs with Queries

Problem
This work addresses the gap in the literature regarding the agnostic learning of general ReLU (Rectified Linear Unit) functions under the Gaussian distribution, specifically in the interactive learning setting. Previous research has established efficient algorithms for passive learning, but there has been limited exploration of how query access to labels can enhance learning efficiency. The authors present their findings in a preprint format, indicating that the work is unreviewed.

Method
The authors propose a computationally efficient learner that operates in an interactive setting, utilizing black-box label queries. The algorithm achieves a query complexity of (d \cdot \text{polylog}(1/\epsilon) + \tilde{O}(\min{1/p, 1/\epsilon})), where (d) is the dimensionality of the input space, (\epsilon) is the error tolerance, and (p) represents the bias of the target function. The learner outputs a hypothesis with an error of (O(opt) + \epsilon), where (opt) is the squared loss of the best-fitting ReLU function. The authors also demonstrate that their query complexity is qualitatively near-optimal, suggesting that the proposed method is efficient in terms of both computational resources and label usage.

Results
The proposed algorithm significantly reduces the number of required label queries compared to passive learning methods. Specifically, it achieves a query complexity of (d \cdot \text{polylog}(1/\epsilon) + \tilde{O}(\min{1/p, 1/\epsilon})), which is a marked improvement over the (\tilde{\Omega}(d/\epsilon)) label requirement for passive learners. The authors provide empirical results that validate the effectiveness of their approach, although specific numerical results against named baselines are not detailed in the abstract.

Limitations
The authors acknowledge that their results are contingent on the assumption of query access to labels, which may not always be feasible in practical scenarios. Additionally, while the query complexity is shown to be near-optimal, the authors do not explore the implications of computational constraints in detail. The necessity of drawing a super-polynomial number of unlabeled examples for any active learner to improve upon passive learning is also flagged as a limitation.

Why it matters
This research has significant implications for the field of machine learning, particularly in the context of active learning and the efficient training of neural networks with ReLU activations. By demonstrating that query access can substantially reduce label complexity, the findings encourage further exploration of interactive learning paradigms. This work lays the groundwork for future studies that may seek to refine active learning strategies, as published in arXiv cs.LG.