The optimal overfitting bias for multiclass classification with k accuracy queries is Theta_tilde(max(sqrt(k/(mn)), k/n)), and the paper gives polynomial-time algorithms achieving it.
Algorithmic stability for adaptive data analysis
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Optimal multiclass overfitting by sequence reconstruction from Hamming queries
The optimal overfitting bias for multiclass classification with k accuracy queries is Theta_tilde(max(sqrt(k/(mn)), k/n)), and the paper gives polynomial-time algorithms achieving it.