  In this note, we investigate the robustness of Nash equilibria (NE) in
multi-player aggregative games with coupling constraints. There are many
algorithms for computing an NE of an aggregative game given a known aggregator.
When the coupling parameters are affected by uncertainty, robust NE need to be
computed. We consider a scenario where players' weight in the aggregator is
unknown, making the aggregator kind of "a black box". We pursue a suitable
learning approach to estimate the unknown aggregator by proposing an inverse
variational inequality-based relationship. We then utilize the counterpart to
reconstruct the game and obtain first-order conditions for robust NE in the
worst case. Furthermore, we characterize the generalization property of the
learning methodology via an upper bound on the violation probability.
Simulation experiments show the effectiveness of the proposed inverse learning
approach.
