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A Query Algorithm for Agnostically Learning DNF?

Motivation: One of the most celebrated results in computational learning theory is Jackson’s query algorithm for PAC learning DNF formulas with respect to the uniform distribution [3]. A natural question is whether DNF formulas can be learned (even with queries and with respect to the uniform distribution) in a highly noisy setting, i.e., the wellknown agnostic framework of learning [5]. Additionally, it is straightforward to see that an agnostic learning algorithm for DNF formulas would give algorithms for weakly learning polynomial-size depth-3 circuits with respect to the uniform distribution in the standard PAC learning model. Halfspaces are another simple and important concept class of functions still not known to be agnostically learnable with respect to the uniform distribution, even if the learner can make queries (although some relevant work exists for the uniform distribution that we mention below).