Provable Sample Complexity Guarantees for Learning of Continuous-Action Graphical Games with Nonparametric Utilities
This provides a theoretical foundation for analyzing complex multi-agent systems, though it is incremental in extending existing methods to nonparametric settings.
The paper tackles the problem of learning the exact structure of continuous-action graphical games with nonparametric utility functions, achieving recovery with a logarithmic sample complexity in terms of the number of players and polynomial runtime.
In this paper, we study the problem of learning the exact structure of continuous-action games with non-parametric utility functions. We propose an $\ell_1$ regularized method which encourages sparsity of the coefficients of the Fourier transform of the recovered utilities. Our method works by accessing very few Nash equilibria and their noisy utilities. Under certain technical conditions, our method also recovers the exact structure of these utility functions, and thus, the exact structure of the game. Furthermore, our method only needs a logarithmic number of samples in terms of the number of players and runs in polynomial time. We follow the primal-dual witness framework to provide provable theoretical guarantees.