  In multi-agent problems requiring a high degree of cooperation, success often
depends on the ability of the agents to adapt to each other's behavior. A
natural solution concept in such settings is the Stackelberg equilibrium, in
which the ``leader'' agent selects the strategy that maximizes its own payoff
given that the ``follower'' agent will choose their best response to this
strategy. Recent work has extended this solution concept to two-player
differentiable games, such as those arising from multi-agent deep reinforcement
learning, in the form of the \textit{differential} Stackelberg equilibrium.
While this previous work has presented learning dynamics which converge to such
equilibria, these dynamics are ``coupled'' in the sense that the learning
updates for the leader's strategy require some information about the follower's
payoff function. As such, these methods cannot be applied to truly
decentralised multi-agent settings, particularly ad hoc cooperation, where each
agent only has access to its own payoff function. In this work we present
``uncoupled'' learning dynamics based on zeroth-order gradient estimators, in
which each agent's strategy update depends only on their observations of the
other's behavior. We analyze the convergence of these dynamics in general-sum
games, and prove that they converge to differential Stackelberg equilibria
under the same conditions as previous coupled methods. Furthermore, we present
an online mechanism by which symmetric learners can negotiate leader-follower
roles. We conclude with a discussion of the implications of our work for
multi-agent reinforcement learning and ad hoc collaboration more generally.
