Optimal Hardness Results for Maximizing Agreements with Monomials

We consider the problem of finding a monomial (or a term) that maximizes the agreement rate with a given set of examples over the Boolean hypercube. The problem is motivated by learning of monomials in the agnostic framework of Haussler [12] and Kearns et al. [17]. Finding a monomial with the highest agreement rate was proved to be NP-hard by Kearns and Li [15]. Ben-David et al. gave the first inapproximability result for this problem, proving that the maximum agreement rate is NP-hard to approximate within 770 767 - , for any constant > 0 [5]. The strongest known hardness of approximation result is due to Bshouty and Burroughs, who proved an inapproximability factor of 59 58 - [8]. We show that the agreement rate is NPhard to approximate within 2 - for any constant > 0. This is optimal up to the second order terms and resolves an open question due to Blum [6]. We extend this result to = 2- log1n for any constant > 0 under the assumption that NP RTIME(npoly log(n) ), thus a...

• Type: Conference
• Year: 2006
• Where: COCO
• Authors: Vitaly Feldman
• Keywords: Agreement Rate, Algorithms, COCO 2006, Inapproximability Factor, Maximum Agreement Rate