Abasic question inlearning theory istoidentify iftwodistributions areidentical when we have access only to examples sampled from the distributions.

Our main algorithmic result is the first query-efficient algorithm for learning halfspaces under the popular Massart noise model.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Intheadversarialsetting,weintroduce the notion ofadversarial VC-dimensionwhich is the VC-dimension of the corrupted hypothesis class.

We introduce the problem of learning conditional averages in the PAC framework. The learner receives a sample labeled by an unknown target concept from a known concept class, as in standard PAC learning. However, instead of learning the target concept itself, the goal is to predict, for each instance, the average label over its neighborhood -- an arbitrary subset of points that contains the instance. In the degenerate case where all neighborhoods are singletons, the problem reduces exactly to classic PAC learning. More generally, it extends PAC learning to a setting that captures learning tasks arising in several domains, including explainability, fairness, and recommendation systems. Our main contribution is a complete characterization of when conditional averages are learnable, together with sample complexity bounds that are tight up to logarithmic factors. The characterization hinges on the joint finiteness of two novel combinatorial parameters, which depend on both the concept class and the neighborhood system, and are closely related to the independence number of the associated neighborhood graph.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Analyzing the convergence properties of these algorithms can be complex, especially for NAG whose convergence proof relies on algebraic tricks that reveal little detail about the acceleration phenomenon, i.e. the celebrated optimality of NAG in convex smooth optimization. Instead, an alternative approach is to view these methods as numerical integrators of some ordinary differential equations (ODEs).