We study the iteration complexity of decentralized learning of approximate correlated equilibria in incomplete information games. On the negative side, we prove that in $\mathit{extensive}$-$\mathit{form}$ $\mathit{games}$, assuming $\mathsf{PPAD} \not\subset \mathsf{TIME}(n^{\mathsf{polylog}(n)})$, any polynomial-time learning algorithms must take at least $2^{\log_2^{1-o(1)}(|\mathcal{I}|)}$ iterations to converge to the set of $\epsilon$-approximate correlated equilibrium, where $|\mathcal{I}|$ is the number of nodes in the game and $\epsilon > 0$ is an absolute constant. This nearly matches, up to the $o(1)$ term, the algorithms of [PR'24, DDFG'24] for learning $\epsilon$-approximate correlated equilibrium, and resolves an open question of Anagnostides, Kalavasis, Sandholm, and Zampetakis [AKSZ'24]. Our lower bound holds even for the easier solution concept of $\epsilon$-approximate $\mathit{coarse}$ correlated equilibrium On the positive side, we give uncoupled dynamics that reach $\epsilon$-approximate correlated equilibria of a $\mathit{Bayesian}$ $\mathit{game}$ in polylogarithmic iterations, without any dependence of the number of types. This demonstrates a separation between Bayesian games and extensive-form games.

翻译：我们研究了不完全信息博弈中近似相关均衡去中心化学习的迭代复杂性。在负面结果方面，我们证明在$\mathit{扩展式博弈}$中，若假设$\mathsf{PPAD} \not\subset \mathsf{TIME}(n^{\mathsf{polylog}(n)})$，则任何多项式时间学习算法至少需要$2^{\log_2^{1-o(1)}(|\mathcal{I}|)}$次迭代才能收敛到$\epsilon$-近似相关均衡集合，其中$|\mathcal{I}|$为博弈节点数，$\epsilon > 0$为绝对常数。该下界与[PR'24, DDFG'24]中学习$\epsilon$-近似相关均衡的算法结果（仅相差$o(1)$项）近乎匹配，并解决了Anagnostides、Kalavasis、Sandholm和Zampetakis [AKSZ'24]提出的公开问题。我们的下界甚至对于更易求解的$\epsilon$-近似$\mathit{粗}$相关均衡概念同样成立。在正面结果方面，我们提出了非耦合动态过程，可在多对数迭代次数内达到$\mathit{贝叶斯博弈}$的$\epsilon$-近似相关均衡，且迭代次数与类型数量无关。这揭示了贝叶斯博弈与扩展式博弈之间的分离性。