We prove some new concentration inequalities for self-bounding functions using the entropy method. As an application, we recover Talagrand's convex distance inequality. The new Bernstein-like inequalities for self-bounding functions are derived thanks to a careful analysis of the so-called Herbst argument. The latter involves comparison results between solutions of differential inequalities that may be interesting in their own right.
"On concentration of self-bounding functions." Electron. J. Probab. 14 1884 - 1899, 2009. https://doi.org/10.1214/EJP.v14-690