I've been reading some papers on reinforcement learning.

$$\Delta w=\frac{\partial ln\ p_w}{\partial w}r$$

I often see expressions, similar to the above one, where the weights (denoted by $$w$$) are updated following the partial derivative of the policy function (denoted by $$p_w$$) with respect to its weights.

But why do we take the $$\log$$? What is its purpose?

1. Maximizing $\log \Phi(x)$ is equivalent to maximizing $\Phi(x)$, so in maximum-likelihood problems, we can maximize the log of the likelihood instead of maximizing the likelihood directly and the result will be equivalent.
• I think you should have been more specific to this context. You should have answered to the questions: 1) How is $\pi_w$ is usually represented and thus derived? 2) Why does $\ln \pi_w$ is a simpler to derive than $\pi_w$? – nbro Feb 19 '19 at 10:41