CSE 599 i : Online and Adaptive Machine Learning Winter 2018 Lecture 6 : Non - stochastic best arm identification

Example 1. Imagine that we are solving a non-convex optimization problem on some (multivariate) function f using gradient descent. Recall that gradient descent converges to local minima. Because non-convex functions may have multiple minima, we cannot guarantee that gradient descent will converge to the global minimum. To resolve this issue, we will use random restarts, the process of starting multiple instances of gradient descent from random locations and outputting the least-valued minimum found. If an instance of gradient descent is obviously not going to converge quickly to a low-valued minimum, that instance should be stopped early in favor of other, more-promising ones.