Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: <lb>Many canonical machine learning problems boil down to a convex optimization problem with a finite<lb>sum structure. However, whereas much progress has been made in developing faster algorithms for<lb>this setting, the inherent limitations of these problems are not satisfactorily addressed by existing lower<lb>bounds. Indeed, current bounds focus on first-order optimization algorithms, and only apply in the often<lb>unrealistic regime where the number of iterations is less than O(d/n) (where d is the dimension and n<lb>is the number of samples). In this work, we extend the framework of Arjevani et al. [3, 5] to provide<lb>new lower bounds, which are dimension-free, and go beyond the assumptions of current bounds, thereby<lb>covering standard finite sum optimization methods, e.g., SAG, SAGA, SVRG, SDCA without duality, as<lb>well as stochastic coordinate-descent methods, such as SDCA and accelerated proximal SDCA.

Dimension-Free Iteration Complexity of Finite Sum Optimization Problems