Sequential PAC learning
Dale Schuurmans, Russell Greiner · 1995
We consider the use of "on-line" stopping rules to reduce the number of training examples needed to pac-learn. Rather than collect a large training sample that can be proved sufficient to eliminate all bad hypotheses a priori, the idea is instead to observe training examples one-at-a-time and decide "on-line" whether to stop and return a hypothesis, or continue training. The primary benefit of this approach is that we can detect when a hypothesizer has actually "converged," and halt training before the standard fixed-sample-size bounds. This paper presents a series of such sequential learning procedures for: distribution-free pac-learning, "mistake-bounded to pac" conversion, and distribution-specific pac-learning, respectively. We analyze the worst case expected training sample size of these procedures, and show that this is often smaller than existing fixed sample size bounds --- while providing the exact same worst case pac-guarantees. We also provide lower bounds that show these r...