Majority-of-Three: The Easiest Optimum Learner?


arXiv:2403.08831v1 Announce Kind: new
Summary: Creating an optimum PAC studying algorithm within the realizable setting, the place empirical danger minimization (ERM) is suboptimal, was a significant open drawback in studying idea for many years. The issue was lastly resolved by Hanneke a number of years in the past. Sadly, Hanneke’s algorithm is sort of advanced because it returns the bulk vote of many ERM classifiers which are skilled on rigorously chosen subsets of the information. It’s thus a pure objective to find out the best algorithm that’s optimum. On this work we examine the arguably easiest algorithm that could possibly be optimum: returning the bulk vote of three ERM classifiers. We present that this algorithm achieves the optimum in-expectation sure on its error which is provably unattainable by a single ERM classifier. Moreover, we show a near-optimal high-probability sure on this algorithm’s error. We conjecture that a greater evaluation will show that this algorithm is in truth optimum within the high-probability regime.

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