I have a reward function $R:\mathbb{R}^6 \to \mathbb{R}$ and I can maximize it using the gradient ascent method. Any suggestion on how to visualize $R$ so that I can get some insight regarding its shape?
One obvious way is isolating the coordinates and generating separate plots but would this help to get an understanding of its overall shape?
As a side note, $R(\xi)$ is in fact cross-correlation between two continuous functions $f_1,f_2:\mathbb{R}^3 \to \mathbb{R}$ and $\xi \in \mathfrak{se}(3)$ is an element of a Lie algebra acting on $\mathbb{R}^3$. Hence, $\xi$ is the decision variable of optimization.