The paper studies the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. The main algorithmic result is a polynomial-time PAC learning algorithm for this concept class in the strong contamination model under the Gaussian distribution, with an error guarantee of Od,c(opt^(1-c)), for any desired constant c > 0, where opt is the fraction of corruptions.
The algorithm employs an iterative approach inspired by localization techniques previously used in the context of learning linear threshold functions. Specifically, it uses a robust perceptron algorithm to compute a good partial classifier and then iterates on the unclassified points. To achieve this, the paper develops new polynomial decomposition techniques, introducing the notion of "super non-singular" polynomial decompositions.
The key technical contributions are:
By combining these components, the paper presents the first polynomial-time algorithm that can robustly learn degree-d PTFs with error Oc,d(1) opt^(1-c) under the Gaussian distribution, for any constant c > 0.
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by Ilias Diakon... om arxiv.org 04-02-2024
https://arxiv.org/pdf/2404.00529.pdfDiepere vragen