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Lemma C.3.Forany 14 : KL(12,12 ) 3 2. Proof.Bydefinitionkl(p, q)= plog (p /q)+( 1 p) log (1 p1 q), so KL 1 2 , 1 2 = 1 2 log ( 1 1 2 ) + log ( 1 1 + 2 ) Exp3 is(U, , T) bounded U(t, )= O( p tklogtk ). Let = Tx 1 +(y x)/2.