# Updating variables in multi variables gradient descent

In gradient descent of a function F($\theta_1$,$\theta_2$), in the update step after doing $\theta_1' \leftarrow \theta_1 - \alpha \frac{\sigma F}{\sigma\theta_1}$ when we update $\theta_2$, do we use the old value of $\theta_1$ or we use the updated one $\theta_1'$?

Edit: Do we use the same $\alpha$ step size for both $\theta_1$ and $\theta_2$?

• @Sally thank you. just fixed it. – user3639557 Feb 18 '16 at 1:12

## 1 Answer

Often you will see the update written will all $\theta$s together as $$\pmb{\theta}' \gets \pmb{\theta}-\mathbf{\alpha}\frac{\partial \mathbf{F}}{\partial \pmb{\theta}}$$ indicating that both happen simultaneously (use the old value) and use the same value $\alpha$.