  In this paper, we study a few challenging theoretical and numerical issues on
the well known trust region policy optimization for deep reinforcement
learning. The goal is to find a policy that maximizes the total expected reward
when the agent acts according to the policy. The trust region subproblem is
constructed with a surrogate function coherent to the total expected reward and
a general distance constraint around the latest policy. We solve the subproblem
using a preconditioned stochastic gradient method with a line search scheme to
ensure that each step promotes the model function and stays in the trust
region. To overcome the bias caused by sampling to the function estimations
under the random settings, we add the empirical standard deviation of the total
expected reward to the predicted increase in a ratio in order to update the
trust region radius and decide whether the trial point is accepted. Moreover,
for a Gaussian policy which is commonly used for continuous action space, the
maximization with respect to the mean and covariance is performed separately to
control the entropy loss. Our theoretical analysis shows that the deterministic
version of the proposed algorithm tends to generate a monotonic improvement of
the total expected reward and the global convergence is guaranteed under
moderate assumptions. Comparisons with the state-of-the-art methods demonstrate
the effectiveness and robustness of our method over robotic controls and game
playings from OpenAI Gym.
