Uniform error bounds for quantized dynamical models

TL;DR

This paper establishes statistical guarantees for the accuracy of quantized dynamical models learned from dependent data, providing uniform error bounds that account for hardware constraints and practical optimization algorithms.

Contribution

It introduces novel uniform error bounds for quantized models, applicable to hybrid system identification, with both slow-rate and fast-rate bounds derived through innovative strategies.

Findings

Bounds scale with encoding bits, linking hardware constraints to statistical complexity

Develops both slow-rate and fast-rate error bounds for quantized models

Applicable to practical system identification scenarios

Abstract

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.