Improved Rates for Derivative Free Gradient Play in Strongly Monotone Games

The influential work of Bravo et al. [1] shows that derivative free gradient play in strongly monotone games has complexity O(d²/ε³), where ε is the target accuracy on the expected squared distance to the solution. This paper shows that the efficiency estimate is actually O(d²/ε²), which reduces to the known efficiency guarantee for the method in unconstrained optimization. The argument we present simply interprets the method as stochastic gradient play on a slightly perturbed strongly monotone game to achieve the improved rate.