An improved uniform convergence bound with fat-shattering dimension

The fat-shattering dimension characterizes the uniform convergence property of real-valued function classes. The state-of-the-art upper bounds in Bartlett and Long (1995) feature a multiplicative squared logarithmic factor on the sample complexity, leaving an open gap with the existing lower bound. By relying on a refined packing number bound given in Rudelson and Vershynin (2006), we provide an improved uniform convergence bound that closes this gap.