Question

In gradient descent, which specific mathematical property of a loss function guarantees that the algorithm will converge to a global minimum rather than getting stuck in a local one?

Accepted Answer

The mathematical property that guarantees gradient descent will converge to a global minimum is convexity. A loss function is convex if a line segment drawn between any two points on the function&#x27;s graph lies entirely on or above the graph. Visually, a convex function is shaped like a bowl, meaning it has only one bottom point, which is the global minimum. Because there are no hills or local valleys in a convex landscape, the gradient, which represents the slope or direction of steepest ascent, always points toward the single lowest point. In non-convex functions, which contain multiple peaks and valleys, gradient descent can become trapped in a local minimum, a low point that is not the absolute lowest point of the function, because the slope at that location becomes zero. When a function is strictly convex, the derivative is zero only at the global minimum, ensuring that once the algorithm reaches a point where the slope is zero, it has arrived at the best possible solution.

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In gradient descent, which specific mathematical property of a loss function guarantees that the algorithm will converge to a global minimum rather than getting stuck in a local one?