Enhanced $H$-Consistency Bounds
Existing H-consistency bounds rely heavily on strong convexity assumptions, limiting their applicability and yielding loose guarantees. Method: We propose a generalized conditional regret inequality framework that—without requiring the surrogate loss lower bound to be convex—derives tighter H-consistency bounds under broader, non-convex settings with predictor- and instance-dependent conditions. By precisely modeling finite-sample relationships between surrogate and target losses (e.g., 0–1 loss) and integrating functional inequalities with statistical learning theory, we obtain unified, improved bounds. Contribution/Results: Our framework encompasses standard multiclass classification, binary/multiclass classification under Tsybakov noise, and bipartite ranking. It substantially enhances both the tightness and generality of theoretical guarantees, overcoming key limitations of prior work while extending H-consistency analysis to previously intractable non-convex and heterogeneous regimes.