  This paper presents a constrained policy gradient algorithm. We introduce
constraints for safe learning with the following steps. First, learning is
slowed down (lazy learning) so that the episodic policy change can be computed
with the help of the policy gradient theorem and the neural tangent kernel.
Then, this enables us the evaluation of the policy at arbitrary states too. In
the same spirit, learning can be guided, ensuring safety via augmenting episode
batches with states where the desired action probabilities are prescribed.
Finally, exogenous discounted sum of future rewards (returns) can be computed
at these specific state-action pairs such that the policy network satisfies
constraints. Computing the returns is based on solving a system of linear
equations (equality constraints) or a constrained quadratic program (inequality
constraints, regional constraints). Simulation results suggest that adding
constraints (external information) to the learning can improve learning in
terms of speed and transparency reasonably if constraints are appropriately
selected. The efficiency of the constrained learning was demonstrated with a
shallow and wide ReLU network in the Cartpole and Lunar Lander OpenAI gym
environments. The main novelty of the paper is giving a practical use of the
neural tangent kernel in reinforcement learning.
