Quantized Online LQR
Barron Han, Victoria Kostina, Babak Hassibi

TL;DR
This paper introduces a rate-efficient online LQR control method that transmits learned system dynamics instead of raw states, achieving near-optimal regret bounds under communication constraints.
Contribution
The paper proposes the QCE-LQR algorithm that matches fundamental information-theoretic lower bounds, improving control performance under limited communication.
Findings
QCE-LQR achieves regret close to unquantized baseline.
The algorithm matches the lower bound of (log T) bits for (T^lpha) regret.
Numerical experiments confirm near-optimal performance on benchmark systems.
Abstract
We study online linear-quadratic regulation (LQR) with unknown dynamics under communication rate constraints. Classical networked control quantizes the plant state at every time step, requiring total bits while injecting persistent quantization noise that limits control performance. We consider a setting where the plant observes its state locally and can estimate system dynamics via ordinary least squares, while a remote controller possesses knowledge of the control cost. Rather than quantizing the raw state, the plant transmits learned dynamics estimates over a rate-limited uplink, and the controller returns the optimal control policy so that the plant can compute actions locally using its superior state knowledge. We first prove a fundamental information-theoretic lower bound: any scheme achieving regret for compared to the optimal infinite…
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