Improved Learning of k-Parities

We consider the problem of learning k-parities in the online mistake-bound model: given a hidden vector \(x \in \{0,1\}^n\) where the hamming weight of x is k and a sequence of “questions” \(a_1, a_2, \dots \in \{0,1\}^n\), where the algorithm must reply to each question with \(\langle a_i, x\rangle \pmod 2\), what is the best trade-off between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et al. [BGM10] by an \(\exp (k)\) factor in the time complexity.

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