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 Ω(T^2/3) for any algorithm discretizes the state space, improving the previous regret bound of Ω(T^1/2) of Ortner and Ryabko [1] for the same problem. Next,under the assumption that the rewards and transitions are Hölder Continuous we show that the upper bound on the discretization error is const.Ln^-α T. Finally,we give some simple experiments to validate our propositions.