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Found 2 papers, 1 papers with code
Online Convex Optimization with Switching Cost and Delayed Gradients
In addition, we show that the competitive ratio of any online algorithm is $\max\{\Omega(L), \Omega(\frac{L}{\sqrt{\mu}})\}$ in the limited information setting when the switching cost is quadratic.
Sharpened Lazy Incremental Quasi-Newton Method
Specifically, they exhibit a superlinear rate with $O(d^2)$ cost in contrast to the linear rate of first-order methods with $O(d)$ cost and the quadratic rate of second-order methods with $O(d^3)$ cost.
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