Computationally Efficient Collaborative Communication Via Regularity-Based Coarsening

2026-08-05

AI Summary

This work addresses the problem of approximating optimal utility in multi-agent coordination with minimal communication. It introduces a novel approach based on the Frieze–Kannan weak regularity lemma, which avoids strong assumptions such as informational substitutability. By coarsening the observation space into a constant-sized partition, the original game is transformed into a coarse game that can be solved efficiently. The resulting protocol runs in time polynomial in the number of agents $n$, actions $m$, and $1/\varepsilon$, while incurring only $2^{O(CC_\alpha(G))}/\varepsilon^2$ bits of communication. Under the assumption that P≠NP, this communication complexity nearly matches the theoretical lower bound, marking the first efficient communication protocol for this setting that does not rely on strong structural assumptions.

Abstract

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.

Problem

• collaborative communication
• communication complexity
• multi-agent information aggregation
• computationally efficient protocols
• regularity-based coarsening

Innovation

• regularity-based coarsening
• communication complexity
• collaborative communication
• Frieze-Kannan regularity
• polynomial-time algorithm