Availability and dimensional requirements of public coordination channels

Quantify when a public coordination channel is available for deployment of the shared-randomness variant of MoSDOT and determine how much shared signal dimension is required.

Background

The paper identifies a strict-product execution constraint in decentralized multi-agent policies: independently sampled local actions cannot represent arbitrary correlated joint-action supports, even when the centralized teacher is perfect. The proposed shared-randomness variant addresses this limitation for joint distributions representable as mixtures of product distributions by providing agents with a public coordination signal while preserving local computation and avoiding observation, action, or message exchange.

However, deployment environments may not permit such a public coordination channel. The unresolved problem is therefore to characterize the conditions under which shared execution signals are available or admissible, and to establish the amount of shared information needed to represent the relevant correlated joint support.