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Approximating Concavely Parameterized Optimization Problems

Approximating Concavely Parameterized Optimization Problems

This video was recorded at 26th Annual Conference on Neural Information Processing Systems (NIPS), Lake Tahoe 2012. We consider an abstract class of optimization problems that are parameterized concavely in a single parameter, and show that the solution path along the parameter can always be approximated with accuracy ε>0 by a set of size O(1/ε). A lower bound of size Ω(1/ε) shows that the upper bound is tight up to a constant factor. We also devise an algorithm that calls a step-size oracle and computes an approximate path of size O(1/ε). Finally, we provide an implementation of the oracle for soft-margin support vector machines, and a parameterized semi-definite program for matrix completion.

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