Computer Scientists Find a Key Research Algorithm's Limits

Computer Scientists Find a Key Research Algorithm's Limits

The most widely used technique for optimizing values of a math function turns out to be a fundamentally difficult computational problem.

MANY ASPECTS OF modern applied research rely on a crucial algorithm called gradient descent. This is a procedure generally used for finding the largest or smallest values of a particular mathematical function a process known as optimizing the function. It can be used to calculate anything from the most profitable way to manufacture a product to the best way to assign shifts to workers. Yet despite this widespread usefulness, researchers have never fully understood which situations the algorithm struggles with most. Now, new work explains it, establishing that gradient descent, at heart, tackles a fundamentally difficult computational problem. The new result places limits on the type of performance researchers can expect from the technique in particular applications.

Gradient descent is an essential tool of modern applied research, but there are many common problems for which it does not work well. But before this research, there was no comprehensive understanding of exactly what makes gradient descent struggle and when questions another area of computer science known as computational complexity theory helped to answer.

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