Learning in the Presence of Malicious Errors

In this paper we study an extension of the distribution-free model of learning introduced by Valiant [23] (also known as the probably approximately correct or PAC model) that allows the presence of malicious errors in the examples given to a learning algorithm. Such errors are generated by an adversary with unbounded computational power and access to the entire history of the learning algorithm's computation. Thus, we study a worst-case model of errors. Our results include general methods for bounding the rate of error tolerable by any learning algorithm, e cient algorithms tolerating nontrivial rates of malicious errors, and equivalences between problems of learning with errors and standard combinatorial optimization problems.