Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, May 31, 2022, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Stefan Tiegel

Optimal SQ Lower Bounds for Learning Halfspaces with Massart Noise

We give tight statistical query (SQ) lower bounds for learning halfspaces in the presence of Massart noise, in which the label of each example x is flipped with a fixed probability depending on x. In particular, suppose that all labels are corrupted with probability at most η. We show that for arbitrary η∈[0,1/2] every SQ algorithm achieving misclassification error better than η requires queries of superpolynomial accuracy or at least a superpolynomial number of queries. Further, this continues to hold even if the information-theoretically optimal error OPT is as small as exp(−logc(d)), where d is the dimension and 0

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