# Distribution-Independent Reliable Learning

We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than other types. A positive reliable classifier is one that makes no false positive errors. The goal in the positive reliable agnostic framework is to output a hypothesis with the following properties: (i) its false positive error rate is at most $\epsilon$, (ii) its false negative error rate is at most $\epsilon$ more than that of the best positive reliable classifier from the class. A closely related notion is fully reliable agnostic learning, which considers partial classifiers that are allowed to predict unknown'' on some inputs. The best fully reliable partial classifier is one that makes no errors and minimizes the probability of predicting unknown'', and the goal in fully reliable learning is to output a hypothesis that is almost as good as the best fully reliable partial classifier from a class.