On the Di cultyof Approximately Maximizing Agreements

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Smart "Predict, then Optimize" (2017, methodology): “Moreover, since Proposition 1 demonstrates that our framework captures binary classiﬁcation, solving (3) is at least as diﬃcult as optimizing the 0-1 loss function, which may be NP-hard in many cases (Ben-David et al. 2003).”
On Symmetric Losses for Learning from Corrupted Labels (2019, unknown): “The main motivation to use a surrogate loss in binary classiﬁcation is that the zero-one loss is discontinuous and therefore diﬃcult to optimize [Ben-David et al., 2003; Feldman et al., 2012].”
On the Consistency of Ordinal Regression Methods (2014, background): “Second, due to the nonconvexity and discontinuity of `, the risk is dicult to optimize and can lead to NP-hard problems [3, 8] (note that binary classication can be seen as a particular case of ordinal regression).”
Complexity theoretic limitations on learning halfspaces (2015, background): “Later on, the corresponding maximization problem was considered by several authors [4, 17, 23, 41, 38], culminating with Feldman, Gopalan, Khot and Ponnuswami [38] who showed that assuming that no quasi-polynomial time algorithm can solve N P hard problems, no eﬃcient algorithm can distinguish…”