New Algorithm for Learning ReLU Functions with Fewer Labeled Examples Using Query Access
Researchers have developed the first computationally efficient algorithm for agnostically learning general ReLU functions using a near-optimal number of label queries, accepted at NeurIPS 2025. The work addresses the interactive learning setting, where a learner can query labels for unlabeled examples, achieving error O(opt)+ε with dramatically fewer labeled examples than passive learning. The results also establish theoretical lower bounds showing that query access is essentially necessary to improve over passive learning label complexity.
The paper presents a new algorithm for robustly learning general (non-homogeneous) ReLU activation functions under the Gaussian distribution with respect to squared loss, operating in an interactive query-based setting rather than passive supervised learning. The algorithm achieves error O(opt)+ε — matching the best possible fit — while requiring only d·polylog(1/ε) + Õ(min{1/p, 1/ε}) black-box label queries, where p is the bias of the target function. This represents a substantial improvement over passive learning, which requires poly(d, 1/ε) labeled examples. The authors complement their upper bound with a matching lower bound, demonstrating that the query complexity is qualitatively near-optimal even without computational constraints. Additionally, they prove a separation result for pool-based active learning: any active learner requires Ω̃(d/ε) labels unless it draws a super-polynomial number of unlabeled examples, establishing that black-box query access is fundamentally more powerful than pool-based active learning for this problem.
What's missing
The paper does not discuss empirical validation on real-world datasets; all results appear to be theoretical. Practical performance under non-Gaussian data distributions and the constants hidden in the O(opt) approximation factor are not addressed.
What different sources said
- arXiv cs.LGCenter
Robust Regression of General ReLUs with Queries
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