alt Hacker NewsJSD is just symmetrized KL, it's the forward KL + reverse KL.
In reinforcement learning, usually what we want is to find the optimal action, i.e. action that maximizes the reward, this translates to the so-called "mode-seeking" optimization, which is the reverse KL.
JSD is slightly different to forward KL + reverse KL (which is unbounded, whereas JSD measured in bits is in the range [0, 1]).
One way to interpret JSD(P, Q): Associate the distributions P and Q with two target classes, respectively. Pick a target class based on a fair coin flip. Then sample either from distribution P or distribution Q, depending on the outcome of the coin flip. The JSD is the mutual information between the resulting mixture distribution and the target class.
Alternative intuition: Suppose we want to measure the correlation between a feature X and a binary target class Y. We have a tabular data set with two columns X and Y, whose rows correspond to individual samples. JSD is the mutual information between the feature X and the target class Y, but after we resample our data (rows) to ensure that we have a balanced representation of the target class Y. If we measure the JSD in bits, the quantity 2^(JSD-1) is the fraction of times X correctly predicts Y, assuming balanced classes.