Assuming that $p,q$ are probability distributions defined on the same support $\{x_i\}_{0 \leq i \leq n}$, $\epsilon$ a small real number, and $D_{KL}$ the Kullback-Leibler divergence,

is there a method or an algorithm to find the set $\mathcal{P}_{q, \epsilon}$ defined as :

$\mathcal{P}_{q, \epsilon}= \{\ p\ |\ D_{KL}(p||q) \leq \epsilon\ \}$

Thank you!