Mendelson, Shahar2015-12-080018-9448http://hdl.handle.net/1885/31331In this correspondence, we present a simple argument that proves that under mild geometric assumptions on the class F and the set of target functions Τ, the empirical minimization algorithm cannot yield a uniform error rate that is faster than 1√k in tKeywords: Control theory; Error analysis; Learning systems; Class-f; Empirical minimization; Error Rate; Function learning; Functionals; Lower bounds; Minimization algorithms; Statistical learning theory; Target functions; Learning algorithms Empirical minimization; Function learning; Lower bounds; Statistical learning theory200810.1109/TIT.2008.9263232015-12-08