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Gradient descent is arguably one of the most popular online optimizationmethods with a wide array of applications. However, the standard implementationwhere agents simultaneously update their strategies yields several undesirableproperties; strategies diverge away from equilibrium and regret grows overtime. In this paper, we eliminate these negative properties by introducing adifferent implementation to obtain finite regret via arbitrary fixed step-size.We obtain this surprising property by having agents take turns when updatingtheir strategies. In this setting, we show that an agent that uses gradientdescent obtains bounded regret -- regardless of how their opponent updatestheir strategies. Furthermore, we show that in adversarial settings thatagents' strategies are bounded and cycle when both are using the alternatinggradient descent algorithm.

Finite Regret and Cycles with Fixed Step-Size via Alternating Gradient Descent-Ascent