It may be “easier to approximate” decentralized infinite-horizon LQG problems

We consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers. It is shown that when two controllers are asymmetric, the linear controller performance can be an arbitrary factor worse than the optimal performance. To fix this problem, we propose a set of nonlinear controllers parameterized by only a few variables, and prove that the proposed set contains an approximately optimal solution that achieves within a constant ratio of the optimal cost. This insight is conveyed using bit-oriented deterministic models that elucidate the nature of the ongoing implicit communication that must occur.