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We consider the problem of control in the setting of reinforcement learning(RL), where model information is not available. Policy gradient algorithms area popular solution approach for this problem and are usually shown to convergeto a stationary point of the value function. In this paper, we propose twopolicy Newton algorithms that incorporate cubic regularization. Both algorithmsemploy the likelihood ratio method to form estimates of the gradient andHessian of the value function using sample trajectories. The first algorithmrequires an exact solution of the cubic regularized problem in each iteration,while the second algorithm employs an efficient gradient descent-basedapproximation to the cubic regularized problem. We establish convergence of ourproposed algorithms to a second-order stationary point (SOSP) of the valuefunction, which results in the avoidance of traps in the form of saddle points.In particular, the sample complexity of our algorithms to find an$\epsilon$-SOSP is $O(\epsilon^{-3.5})$, which is an improvement over thestate-of-the-art sample complexity of $O(\epsilon^{-4.5})$.

A Cubic-regularized Policy Newton Algorithm for Reinforcement Learning