  Consider the problem of training robustly capable agents. One approach is to
generate a diverse collection of agent polices. Training can then be viewed as
a quality diversity (QD) optimization problem, where we search for a collection
of performant policies that are diverse with respect to quantified behavior.
Recent work shows that differentiable quality diversity (DQD) algorithms
greatly accelerate QD optimization when exact gradients are available. However,
agent policies typically assume that the environment is not differentiable. To
apply DQD algorithms to training agent policies, we must approximate gradients
for performance and behavior. We propose two variants of the current
state-of-the-art DQD algorithm that compute gradients via approximation methods
common in reinforcement learning (RL). We evaluate our approach on four
simulated locomotion tasks. One variant achieves results comparable to the
current state-of-the-art in combining QD and RL, while the other performs
comparably in two locomotion tasks. These results provide insight into the
limitations of current DQD algorithms in domains where gradients must be
approximated. Source code is available at https://github.com/icaros-usc/dqd-rl
