  Stackelberg games have been widely used to model interactive decision-making
problems in a variety of domains such as energy systems, transportation,
cybersecurity, and human-robot interaction. However, existing algorithms for
solving Stackelberg games often require knowledge of the follower's cost
function or learning dynamics and may also require the follower to provide an
exact best response, which can be difficult to obtain in practice. To
circumvent this difficulty, we develop an algorithm that does not require
knowledge of the follower's cost function or an exact best response, making it
more applicable to real-world scenarios. Specifically, our algorithm only
requires the follower to provide an approximately optimal action in response to
the leader's action. The inexact best response is used in computing an
approximate gradient of the leader's objective function, with which
zeroth-order bilevel optimization can be applied to obtain an optimal action
for the leader. Our algorithm is proved to converge at a linear rate to a
neighborhood of the optimal point when the leader's cost function under the
follower's best response is strongly convex and smooth.
