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A few improvements

Why do we use the log in gradient-based reinforcement algorithms?

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?

user65539