Provable Sample Complexity Guarantees For Learning Of Continuous-Action Graphical Games With Nonparametric Utilities

Abstract

In this paper, we study the problem of learning the exact structure of continuous-action games with non-parametric utility functions. We propose an ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -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. A full version of this paper is accessible at: https://www.cs.purdue.edu/homes/abarik/abarik_nonpara_icassp_full.pdf