Follower Agnostic Methods for Stackelberg Games

We propose an algorithm to solve a class of Stackelberg games (possibly with multiple followers) in a follower agnostic manner. Particularly, unlike other contemporary works, our algorithm does not require the use of an oracle estimator for the gradient of the leader's objective or knowledge about the follower's utility function or strategy space. Instead, we design two-loop algorithm where the leader updates its strategies using specially constructed gradient estimator obtained by probing followers with specially designed strategies. Upon receiving the followers engage in an adaptation rule such that the joint strategy of followers converges near equilibrium which is the only information observed by leader to construct the aforementioned gradient estimator. We provide non-asymptotic convergence rates to stationary points of the leader's objective in the absence of convexity of the closed-loop function and further show asymptotic convergence to a local minima of the leader's objective.