# Constant Learning Rate for Gradient Decent

Given, we have a learning rate, $$\alpha_n$$ for the $$n^{th}$$ step of the gradient descent process. What would be the impact of using a constant value for $$\alpha_n$$ in gradient descent?

• Do you mean a constant value of $\alpha$ for each step?
– Wes
Feb 11 '19 at 21:18

Intuitively, if $$\alpha$$ is too large you may "shoot over" your target and end up bouncing around the search space without converging. If $$\alpha$$ is too small your convergence will be slow and you could end up stuck on a plateau or a local minimum.
$$\theta_{j} := \theta_{j} - \alpha \frac{\delta}{\delta \theta_{j}} J(\theta)$$
Here $$\theta_{j}$$ is a parameter of your model, and $$J$$ is the cost/loss function. At each step the product $$\alpha \frac{\delta}{\delta \theta_{j}} J(\theta)$$ gets smaller as we get closer to the gradient $$\frac{\delta}{\delta \theta_{j}} J(\theta)$$ converging to 0. $$\alpha$$ can be constant, and in many cases, it is, but varying $$\alpha$$ might help converge faster.