Implicit and explicit communication in decentralized control

TL;DR

This paper investigates how combining implicit and explicit communication in decentralized control can significantly reduce control costs, extending Witsenhausen's counterexample with a rate-limited external channel and proposing a binning-based strategy.

Contribution

It introduces a novel binning-based strategy that outperforms previous methods and proves near-optimality in an extended control problem with an external communication channel.

Findings

Binning-based strategy outperforms previous methods by large factors.

Strategy is within a constant factor of optimal for infinite-length problems.

Approximate optimality achieved for fixed rates, but not uniformly over all rates.

Abstract

There has been substantial progress recently in understanding toy problems of purely implicit signaling. These are problems where the source and the channel are implicit -- the message is generated endogenously by the system, and the plant itself is used as a channel. In this paper, we explore how implicit and explicit communication can be used synergistically to reduce control costs. The setting is an extension of Witsenhausen's counterexample where a rate-limited external channel connects the two controllers. Using a semi-deterministic version of the problem, we arrive at a binning-based strategy that can outperform the best known strategies by an arbitrarily large factor. We also show that our binning-based strategy attains within a constant factor of the optimal cost for an asymptotically infinite-length version of the problem uniformly over all problem parameters and all rates on the external channel. For the scalar case, although our results yield approximate optimality for each fixed rate, we are unable to prove approximately-optimality uniformly over all rates.