  Safe reinforcement learning (RL) is still very challenging since it requires
the agent to consider both return maximization and safe exploration. In this
paper, we propose CUP, a Conservative Update Policy algorithm with a
theoretical safety guarantee. We derive the CUP based on the new proposed
performance bounds and surrogate functions. Although using bounds as surrogate
functions to design safe RL algorithms have appeared in some existing works, we
develop them at least three aspects: (i) We provide a rigorous theoretical
analysis to extend the surrogate functions to generalized advantage estimator
(GAE). GAE significantly reduces variance empirically while maintaining a
tolerable level of bias, which is an efficient step for us to design CUP; (ii)
The proposed bounds are tighter than existing works, i.e., using the proposed
bounds as surrogate functions are better local approximations to the objective
and safety constraints. (iii) The proposed CUP provides a non-convex
implementation via first-order optimizers, which does not depend on any convex
approximation. Finally, extensive experiments show the effectiveness of CUP
where the agent satisfies safe constraints. We have opened the source code of
CUP at https://github.com/RL-boxes/Safe-RL.
