Uniform error bounds for quantized dynamical models
This work addresses the need for interpretable statistical complexities in system identification, particularly for hybrid systems, by translating hardware constraints into error bounds.
The paper tackles the problem of providing statistical guarantees for dynamical models learned from dependent data, specifically for quantized models and imperfect optimization algorithms, by developing uniform error bounds that scale with the number of bits required to encode the model.
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.