基于正则性粗化的计算高效协作通信
Computationally Efficient Collaborative Communication Via Regularity-Based Coarsening
- University of California, Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出基于正则性粗化的高效协作通信协议设计算法，在仅需短高效用协议存在的弱假设下，实现了接近最优的通信效率，并证明了指数依赖的紧性，填补了多智能体信息聚合领域的理论空白。
AI中文摘要：
我们的研究结果表明，短的高效用协议的存在已足以实现高效通信。具体而言，在一个具有$n$种可能观测和$m$个动作的博弈中：(1) 对于任意可实现的目标效用$α$，我们提出了一种运行时间为$\text{poly}(n, m, 1/ε)$的算法，该算法设计的协议仅需使用$2^{\tilde{\text{O}}(CC_α(G))}/ε^2$比特的通信量，就能实现至少$α-ε$的效用。其中，$CC_α(G)$是任意协议（即使是计算低效的协议）实现效用$α$所需的最少比特数。(2) 我们证明了这种对$CC_α(G)$的指数依赖在常数因子范围内是紧的。也就是说，除非$\text{P}=\text{NP}$，否则一般情况下没有多项式时间算法能找到使用少于$2^{CC_α(G) -2}$比特的最优协议。\n我们注意到，我们的结果严格弱化了多智能体信息聚合领域现有工作所需的假设，填补了即使在$CC_α(G)$为常数的博弈中也一直难以解决的空白。具体而言，此前基于共识的信息聚合的性能保证依赖于信息替代或弱可学习性等结构性假设。我们证明这些假设已经隐含$CC_α(G) = O(1)$，因此是比我们的协议成功所需条件更严格的限制。\n在技术层面，我们的结果涉及对Frieze-Kannan弱正则性引理的一种新型强化，并产出了以下强大的多项式时间转换工具：对于每个通信博弈$G$，该工具构造一个博弈$\tilde{G}$，它是将智能体观测空间粗化为常数规模划分的结果，使得$G$和$\tilde{G}$对于所有短通信协议而言都是不可区分的。这一粗化定理是我们算法的核心动力，其本身也可能具有独立研究价值。
英文摘要：
Our results show that the existence of a short high-utility protocol already suffices for efficient communication. In particular, in a game with $n$ possible observations and $m$ actions: (1) For any achievable target utility $α$, we give an algorithm with $\mathrm{poly}(n, m, 1/ε)$ runtime that designs a protocol achieving utility at least $α-ε$ using only $2^{\mathcal O(CC_α(G))}/ε^2$ bits of communication. Here, $CC_α(G)$ is the minimum number of bits used by any protocol, even a computationally inefficient one, to achieve utility $α$. (2) We prove that this exponential dependence on $CC_α(G)$ is tight up to a constant. That is, unless $\mathrm P=\mathrm{NP}$, no polynomial-time algorithm can in general find optimal protocols using fewer than $2^{CC_α(G) -2}$ bits. We note that our results strictly weaken the assumptions required by prior work in the multi-agent information aggregation literature, filling a gap that had remained elusive even for games with constant $CC_α(G)$. In particular, prior guarantees for agreement-based information aggregation rely on structural assumptions such as informational substitutes or weak learnability. We show that these assumptions already imply $CC_α(G) = O(1)$ and are therefore more restrictive conditions than required by our protocol to succeed. On a technical level, our results involve a novel strengthening of the Frieze-Kannan weak regularity lemma and yield the following powerful polynomial-time transformation tool: for every communication game $G$, it constructs a game $\hat G$ that is a coarsening of the agents' observation spaces into constant-size partitions, such that $G$ and $\hat G$ are indistinguishable with respect to every short communication protocol. This coarsening theorem is the engine behind our algorithm and may be of independent interest.
