Complete separation in logistic regression

A linear boundary perfectly separates all training labels. Why might unregularised logistic coefficients fail to converge to a finite estimate?

Along a separating direction, increasing coefficient magnitudes continually improves the likelihood while probabilities approach zero or one. The likelihood supremum can therefore occur only at infinite coefficient norms. Use a regularised fit or an appropriate bias-reduction method and investigate leakage or a small sample. Numerical convergence messages alone do not establish that a finite unregularised maximum exists.