#### Abstract

where RA(T ) is the regret of A and is o(T ). To prove Proposition 4.3, we only need to show that Eqn. 5 holds for some γ ∈ (0, 1]. This is equivalent to showing that there exist a hypothesis h̃ ∈ H (‖h̃‖ = 1), such that 〈h̃, f∗〉 > 0. To see this equivalence, let us assume that 〈h̃, f∗/‖f∗‖〉 = > 0. Let us set h∗ = ‖f∗‖h̃. Using Pythagorean theorem, we can… (More)