Multi-group Agnostic PAC Learnability
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An agnostic PAC learning algorithm finds a predictor that is competitive with the best predictor in a benchmark hypothesis class, where competitiveness is measured with respect to a given loss function. However, its predictions might be quite sub-optimal for structured subgroups of individuals, such as protected demographic groups. Motivated by such fairness concerns, we study "multi-group agnostic PAC learnability": fixing a measure of loss, a benchmark class $̋ and a (potentially) rich collection of subgroups, the objective is to learn a single predictor such that the loss experienced by every groupg ∈is not much larger than the best possible loss for this group within$̋. Under natural conditions, we provide a characterization of the loss functions for which such a predictor is guaranteed to exist. For any such loss function we construct a learning algorithm whose sample complexity is logarithmic in the size of the collection . Our results unify and extend previous positive and negative results from the multi-group fairness literature, which applied for specific loss functions.
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