How do you handle optimization problems with many local minima?

1 Gradient-based methods

One of the most popular methods to optimize a loss function is to use gradient-based methods, such as gradient descent or stochastic gradient descent. These methods update the parameters by moving in the direction of the negative gradient, or the steepest downhill slope, of the loss function. However, gradient-based methods can get stuck in local minima if the gradient becomes zero or very small. To avoid this, you can use some tricks, such as adding momentum, adaptive learning rates, or regularization, to escape from local minima and explore other regions of the parameter space.

2 Random restarts

Another simple technique to handle optimization problems with many local minima is to use random restarts. This means that you run the optimization algorithm multiple times with different initial values for the parameters, and then choose the best solution among them. Random restarts can help you find a global minimum or a better local minimum than the one you started with. However, random restarts can be inefficient and time-consuming, especially if the parameter space is large or the loss function is complex.

5 Bayesian optimization

Bayesian optimization is a method that uses a probabilistic model to guide the search for the optimal solution. The idea is to build a surrogate function that approximates the loss function based on the observed data. Then, the algorithm uses an acquisition function that balances exploration and exploitation to select the next point to evaluate. The algorithm updates the surrogate function and repeats the process until a stopping criterion is met. Bayesian optimization can handle optimization problems with many local minima by learning from the data and focusing on the most promising regions of the parameter space.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?