Another problem about the code

[alba cheng]

I'm reading traj_opt_utils.py, and I'm confused by the computation of KL divergence between new and previous trajectory.It's about the code:

kl_div[t] = max(
    0,
    -0.5 * mu_t.T.dot(M_new - M_prev).dot(mu_t) -
    mu_t.T.dot(v_new - v_prev) - c_new + c_prev -
    0.5 * np.sum(sigma_t * (M_new-M_prev)) - 0.5 * logdet_new +
    0.5 * logdet_prev
)

I cann't figure out  why kl divergence could be computed like this. Any help would be grateful!

[biao sun]

Hi,

Have you found the reason? I am puzzle too.

biao

在 2016年9月24日星期六 UTC+8下午12:26:15，alba cheng写道：

[Victor Barbarosh]

I assume they are making sure the KL-div at each [t] will have a positive value, such that when finally returning the sum(list of values) it won't mess up the result, but it's interesting when we might get negative values...

[Marvin Zhang]

This is computing the KL-divergence between Gaussians, i.e.:

http://stats.stackexchange.com/questions/60680/kl-divergence-between-two-multivariate-gaussians

However, it looks a bit strange here because it is actually computing an expectation of the KL-divergence over x, so it is an integral over D_KL(p(u|x)||\bar{p}(u|x)) p(x) dx. The derivation is relatively complicated.

The max with 0 is just for numerical stability, as Victor suggests.

Marvin

[alba cheng]

Thanks for your reply. To be honest, I still do not understand...M_prev , v_pre, c_pre seems like second derivative of p(tau), first derivative of p(tau) and constant. I think they are second order approximation...Could you give me more details? It would be grateful!