Separating Distribution-Free and Mistake-Bound Learning Models over the Boolean Domain

Two of the most commonly used models in computational learning theory are the distribution-free model in which examples are chosen from a fixed but arbitrary distribution, and the absolute mistake-bound model in which examples are presented in an arbitrary order. Over the Boolean domain {0, 1}n, it is known that if the learner is allowed unlimited computational resources then any concept class learnable in one model is also learnable in the other. In addition, any polynomial-time learning algorithm for a concept class in the mistake-bound model can be transformed into one that learns the class in the distribution-free model. This paper shows that if one-way functions exist, then the mistake-bound model is strictly harder than the distribution-free model for polynomial-time learning. Specifically, given a one-way function, we show how to create a concept class over {0, 1}n that is learnable in polynomial time in the distribution-free model, but not in the absolute mistake-bound model. I...

• Type: Conference
• Year: 1990
• Where: FOCS
• Authors: Avrim Blum
• Keywords: Concept Class, Distribution-free Model, FOCS 1990, Mistake-bound Model, Theoretical Computer Science