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.

中文翻译：

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用于学习具有非参数效用的连续动作图形游戏的可证明样本复杂性保证

在本文中，我们研究了学习具有非参数效用函数的连续动作游戏的确切结构的问题。我们提出了一种 $\ell_1$ 正则化方法，该方法鼓励恢复效用的傅立叶变换系数的稀疏性。我们的方法通过访问很少的纳什均衡及其嘈杂的效用来工作。在某些技术条件下，我们的方法还恢复了这些效用函数的确切结构，从而恢复了游戏的确切结构。此外，我们的方法只需要一个关于玩家数量的对数样本，并在多项式时间内运行。我们遵循原始双重见证框架来提供可证明的理论保证。