Lower Bounds for Higher-Order Convex Optimization
نویسندگان
چکیده
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothness parameters is necessary. As a special case, we show Nesterov’s accelerated cubic regularization method to be nearly tight. [email protected], Computer Science, Princeton University [email protected], Computer Science, Princeton University
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ورودعنوان ژورنال:
- CoRR
دوره abs/1710.10329 شماره
صفحات -
تاریخ انتشار 2017