  We provide a novel dimension-free uniform concentration bound for the
empirical risk function of constrained logistic regression. Our bound yields a
milder sufficient condition for a uniform law of large numbers than conditions
derived by the Rademacher complexity argument and McDiarmid's inequality. The
derivation is based on the PAC-Bayes approach with second-order expansion and
Rademacher-complexity-based bounds for the residual term of the expansion.
