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We propose new restarting strategies for accelerated gradient and acceleratedcoordinate descent methods. Our main contribution is to show that the restartedmethod has a geometric rate of convergence for any restarting frequency, and soit allows us to take profit of restarting even when we do not know the strongconvexity coefficient. The scheme can be combined with adaptive restarting,leading to the first provable convergence for adaptive restarting schemes withaccelerated gradient methods. Finally, we illustrate the properties of thealgorithm on a regularized logistic regression problem and on a Lasso problem.

Restarting accelerated gradient methods with a rough strong convexity estimate