  In many applications, data is collected in batches, some of which are corrupt
or even adversarial. Recent work derived optimal robust algorithms for
estimating discrete distributions in this setting. We consider a general
framework of robust learning from batches, and determine the limits of both
classification and distribution estimation over arbitrary, including
continuous, domains. Building on these results, we derive the first robust
agnostic computationally-efficient learning algorithms for piecewise-interval
classification, and for piecewise-polynomial, monotone, log-concave, and
gaussian-mixture distribution estimation.
