How does Naïve Bayes behave under Bayesian optimal decision boundary convergence?

Naïve Bayes converges toward the Bayes optimal decision boundary under correct model assumptions and sufficient data.

The Bayes optimal classifier minimizes expected classification error using true posterior probabilities. Naïve Bayes approximates this by estimating P(C|X) under independence assumptions. When feature independence holds or errors cancel symmetrically, NB's decision boundary approaches the optimal boundary asymptotically. However, under model misspecification, convergence is biased but often still stable in ranking space.