# What does the notation sup dist mean in distributional RL?

I'm trying to understand distributional RL, based on this article. In one of the equations, there is a symbol $$\operatorname{sup dist}$$.

\begin{align} \operatorname{sup dist}_{s, a} (R(s, a) + \gamma Z(s', a^*), Z(s, a)) \\ s' \sim p(\cdot \mid s, a) \end{align}

What does $$\operatorname{sup dist}$$ mean?

I guess that $$\sup$$ simply refers to the supremum, that is, you want to select actions that maximize the quantity that comes to the right of $$\sup$$, while $$\text{dist}$$ is simply a proxy for any possible distance between distributions. For example, you can replace $$\text{dist}$$ with the Kullback-Leibler divergence or with the mutual information.