Complexity Theoretic Limitations on Learning DNF’s


Amit Daniely, Shai Shalev-Shwartz ;
29th Annual Conference on Learning Theory, PMLR 49:815-830, 2016.


Using the recently developed framework of Daniely, Linial and Shalev-Shwartz, we show that under a natural assumption on the complexity of random K-SAT, learning DNF formulas is hard. Furthermore, the same assumption implies the hardness of various learning problems, including intersections of logarithmically many halfspaces, agnostically learning conjunctions, as well as virtually all (distribution free) learning problems that were previously shown hard (under various complexity assumptions).

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