Distribution-Free Guarantees for Systems with Decision-Dependent Noise
<|reference_start|>Distribution-Free Guarantees for Systems with Decision-Dependent Noise: In many real-world dynamical systems, obtaining precise models of system uncertainty remains a challenge. It may be difficult to estimate noise distributions or robustness bounds, especially when the distributions/robustness bounds vary with different control inputs in unknown ways. Addressing this challenge, this paper presents a novel iterative method tailored for systems with decision-dependent noise without prior knowledge of the distributions. Our approach finds the open-loop control law that minimizes the worst-case loss, given that the noise induced by this control lies in its $(1 - p)$-confidence set for a predetermined $p$. At each iteration, we use a quantile method inspired by conformal prediction to empirically estimate the confidence set shaped by the preceding control law. These derived confidence sets offer distribution-free guarantees on the system's noise, guiding a robust control formulation that targets worst-case loss minimization. Under specific regularity conditions, our method is shown to converge to a near-optimal open-loop control. While our focus is on open-loop controls, the adaptive, data-driven nature of our approach suggests its potential applicability across diverse scenarios and extensions.<|reference_end|>
@article{zhang2024distribution-free,
    title={Distribution-Free Guarantees for Systems with Decision-Dependent Noise},
    author={Heling Zhang, Lillian J. Ratliff, Roy Dong},
    journal={arXiv preprint arXiv:2403.01072},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01072},
    primaryClass={eess.SY cs.SY}
}