Separating Models of Learning with Faulty Teachers

We study the power of two models of faulty teachers in Valiant’s PAC learning model and Angluin’s exact learning model. The first model we consider is learning from an incomplete membership oracle introduced by Angluin and Slonim (1994). In this model, the answers to a random subset of the learner’s membership queries may be missing. The second model we consider is random persistent classification noise in membership queries introduced by Goldman et al. (1993). In this model, the answers to a random subset of the learner’s membership queries are flipped. We show that in both the PAC and the exact learning models the incomplete membership oracle is strictly stronger than the noisy membership oracle under the assumption that the problem of PAC learning parities with random classification noise is intractable. We also show that under the standard cryptographic assumptions the incomplete membership oracle is strictly weaker than the perfect membership oracle. This generalizes the result of Simon (2004) and resolves an open question of Bshouty and Eiron (2002).