A Tractable Algorithm For Finite-Horizon Continuous Reinforcement Learning

We consider the finite horizon continuous reinforcement learning problem. Our contribution is three-fold. First,we give a tractable algorithm based on optimistic value iteration for the problem. Next,we give a lower bound on regret of order Omega(T2/3) for any algorithm discretizes the state space, improving the previous regret bound of Omega(T1/2) of Ortner and Ryabko citecontrl for the same problem. Next,under the assumption that the rewards and transitions are H"older Continuous we show that the upper bound on the discretization error is const.Ln-αT. Finally,we give some simple experiments to validate our propositions.