Gradient Descent: minimum value

Hi! I want to ask a question about gradient descent. How we know if we already in minimum?

Hi @innocentia_h ,

Welcome to the community.

To determine if we have reached the minimum, there are a few common approaches:

  1. Convergence criteria: We can set a threshold for the change in the cost function or the parameters. If the change falls below this threshold, we can consider the algorithm to have converged to a minimum. This approach assumes that the algorithm has reached a point where further iterations will not significantly improve the solution.

  2. Maximum number of iterations: We can set a maximum number of iterations for the algorithm. If the algorithm reaches this limit without satisfying the convergence criteria, we can assume that it has not yet reached the minimum. This approach helps prevent the algorithm from running indefinitely.

  3. Visual inspection: For functions with a low number of dimensions, we can plot the cost function and visually inspect its behavior. If the function reaches a point where it appears to flatten out or stabilize, it may indicate that we have reached a minimum. However, this approach is not feasible for high-dimensional functions.

It’s important to note that gradient descent can sometimes get stuck in local minima, which are suboptimal solutions. To mitigate this, techniques like random restarts or more advanced optimization algorithms can be used.

Remember that gradient descent is an iterative process, and reaching the global minimum (if it exists) is not always guaranteed. The choice of learning rate, initialization, and other hyperparameters can also affect the convergence behavior. Experimentation and careful tuning are often necessary to achieve the best results.

Hope I solved your doubt. If any further doubt please mention. We would be happy to answer.

Regards,
Harsh Der.

If you are at the minimum, you can observe a couple of clues:

  • The gradients will all be nearly zero.
  • The cost will no longer decrease with additional iterations.