# converting tanh activation output to a probability

I am trying to implement $$PPO$$ for continuous action spaces so need probability of taking actions from a neural network with a tanh activation in the output layer since the action space ranges from $$[-2, 2]$$. I multiply the tanh output in the $$[-1,1]$$ range by $$2$$ to get this action.
I saw this: tanh converted to probability

0.5(a(x)+1) converts tanh to a probability.

says it is $$0.5(a(2x) + 1)$$...which I don't really understand if $$a(x)$$ is the $$\tanh$$ output then am I supposed to feed $$2x$$ to the network rather than $$1x$$ just for the purposes of this conversion from $$\tanh$$ to probability?

I do not have enough rep to comment so I posted a new question here.

Both are fine. The idea is to the output of $$a(x)=\tanh(x)$$ to an increasing function that takes value from $$(0,1)$$.

Since for any real number $$x$$, $$-1 \le \tanh(x) \le 1$$

$$0\le \tanh(x) + 1\le 2$$

$$0\le \frac{\tanh(x) + 1}2\le 1$$

You can actually consider the map $$\frac{a(tx)+1}2$$ where $$t$$ is a parameter of your choice that control the variance of your distribution.

You might like to read about the logistic distribution where its CDF is

$$\frac12 + \frac12\tanh\left( \frac{x-\mu}{2s}\right)$$

where its mean is $$\mu$$ and its variance is $$\frac{s^2\pi^2}{3}$$.

• I just read the link for logistic distribution and saw that CDF is used in neural networks. I will try implementing it and the PDF of normal distribution to see which gives best results in the PPO algo. Do you actually recommend CDF more and if so why? – mLstudent33 May 26 '19 at 8:07
• I am not familiar with PPO hence I can't answer the question. I think it depends on the property that you need in your problem, pdf can give you some values that are bigger than $1$ or not able to attain value of $1$ sometimes. – Siong Thye Goh May 26 '19 at 8:40
• I see. I definitely do not want a value bigger than 1 but I think I am okay because I am using a range of two values to approximate the PDF at a given point along the distribution. – mLstudent33 May 26 '19 at 9:39