Flexibility and Cost-Dependence in Quantized Control

Abstract

Layered control architectures in biology and neuroscience can be used to mitigate speed-accuracy tradeoffs, with low-layer quantized controllers carrying out time-sensitive tasks at reduced precision. Here, we describe and optimize the worst-case approximation loss for a quantized controller: the maximum control and state costs paid in the quantized case that would not be paid in the full-precision case. We show that the optimal design of a quantizer depends on the dynamics and the state and control costs, leading notably to cases in which systematically biased estimates of state are optimal for control. We further show that high-layer input can direct a low-layer controller to flexibly execute quantized control across context-related cost functions, with component-level mechanisms that are plausibly implementable in biological settings.