Open Problem: Do Good Algorithms Necessarily Query Bad Points?


Rong Ge, Prateek Jain, Sham M. Kakade, Rahul Kidambi, Dheeraj M. Nagaraj, Praneeth Netrapalli ;
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:3190-3193, 2019.


Folklore results in the theory of Stochastic Approximation indicates the (minimax) optimality of Stochastic Gradient Descent (SGD) (Robbins and Monro, 1951) with polynomially decaying stepsizes and iterate averaging (Ruppert, 1988; Polyak and Juditsky, 1992) for classes of stochastic convex optimization. Basing of these folkore results and some recent developments, this manuscript considers a more subtle question: does any algorithm necessarily (information theoretically) have to query iterates that are sub-optimal infinitely often?

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