Before revision:  For general policy classes, we establish the connection of the regret bound with a generalization of the VC dimension in higher dimensions and specialize this to prove optimal regret bounds for the argmax linear function class{\epsilon})) iteration complexity, where each iteration consists of an SDP feasibility problem and a Newton update using the Nesterov-Todd direction, respectively} .
After revision:  For general policy classes, we establish the connection of the problem of optimal diagonal preconditioning to improve the condition number of any full-rank matrix and provide a bisection algorithm and a potential reduction algorithm with O(\log(\frac{1{\epsilon})) iteration complexity, where each iteration consists of an SDP feasibility problem and a Newton update using the Nesterov-Todd direction, respectively} .