Gradient Descent: The Mother of All Algorithms?
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More than a half of century of research in theoretical computer science brought us a great wealth of advanced algorithmic techniques. These techniques can then be combined in a variety of ways to provide us with sophisticated, often beautifully elegant algorithms. This diversity of methods is truly stimulating and intellectually satisfying. But is it also necessary? In this talk, I will address this question by discussing one of the most, if not the most, fundamental continuous optimization techniques: the gradient descent method. I will briefly describe how this method can be applied, sometime in a quite non-obvious manner, to a number of classic algorithmic tasks, such as the maximum flow problem, the bipartite matching problems, the k-server problem, as well as matrix scaling and balancing. The resulting perspective will provide us with a broad, unifying view on this diverse set of problems. A perspective that was key to making the first in decades progress on each one of these tasks.
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