Distribution-Free Guarantees for Systems with Decision-Dependent Noise

Temel Kavramlar

The authors propose an iterative method to provide distribution-free guarantees for systems with decision-dependent noise, aiming to minimize worst-case loss without prior knowledge of noise distributions.

Özet

The paper introduces a novel iterative method tailored for systems with decision-dependent noise, offering distribution-free guarantees on the system's noise. The approach finds the open-loop control law that minimizes worst-case loss without prior knowledge of noise distributions. By using a quantile method inspired by conformal prediction, the method provides empirical constraints on system disturbance, guiding robust control formulation. The theoretical analysis shows convergence to near-optimal open-loop control under specific regularity conditions.
Traditional strategies like stochastic and robust control often require prior knowledge or assumptions about disturbances, which are not always available in practice. Modern learning-based methods offer less information but lack rigorous guarantees. The proposed method addresses these challenges by providing distribution-free guarantees and minimizing worst-case loss without prior knowledge of disturbances.
The paper also discusses the application of conformal prediction in control tasks and highlights the importance of iterative refinement in dealing with performative prediction problems. The convergence properties of the proposed method are analyzed under various assumptions, providing insights into achieving optimal performance in noisy dynamical systems.

İstatistikler

Ni = O(4λ^2T^3 / β^2δ^2 Σt=0^(T-1) ǫ_t^2 log(6pπ^2i^2T^2))

Alıntılar

"Our approach finds the open-loop control law that minimizes the worst-case loss without prior knowledge of noise distributions."
"The derived confidence sets offer distribution-free guarantees on the system’s noise."
"Our method converges to a near-optimal open-loop control law under specific regularity conditions."

Önemli Bilgiler Şuradan Elde Edildi

Distribution-Free Guarantees for Systems with Decision-Dependent Noise

by Heling Zhang... : arxiv.org 03-05-2024

https://arxiv.org/pdf/2403.01072.pdf

Daha Derin Sorular

How can this iterative methodology be extended to closed-loop controls

To extend this iterative methodology to closed-loop controls, we need to adapt the approach to incorporate feedback from the system's output. In a closed-loop control system, the control input is adjusted based on the system's response, which introduces additional complexity compared to open-loop systems.
One way to extend the methodology is by incorporating state estimation techniques such as Kalman filters or particle filters to estimate the current state of the system based on available measurements. This estimated state can then be used in conjunction with historical data and control inputs to refine the iterative process.
Additionally, in closed-loop systems, stability analysis becomes crucial. The iterative refinement process should ensure that any adjustments made do not destabilize the system but rather lead it towards an optimal operating point while considering performance objectives and constraints.
By integrating feedback mechanisms for adjusting control inputs based on observed outputs and ensuring stability through appropriate analysis and design considerations, this iterative methodology can effectively be extended to closed-loop controls.

What are the implications of assuming no prior knowledge of disturbances in real-world applications

Assuming no prior knowledge of disturbances in real-world applications has significant implications for robustness and adaptability. By eliminating reliance on pre-existing models or assumptions about noise distributions, this approach allows for more flexibility in handling uncertainties inherent in complex dynamical systems.
One key implication is increased resilience against unforeseen variations or changes in disturbances. Real-world environments are dynamic and unpredictable, making it challenging to accurately model all possible sources of disturbance a system may encounter. By adopting a distribution-free approach without prior knowledge requirements, systems can better cope with unexpected scenarios without compromising performance or safety.
Furthermore, by focusing on empirical observations and adaptive learning strategies instead of fixed assumptions about disturbances, this methodology enables continuous improvement and adaptation over time. It promotes a data-driven decision-making process that leverages real-time information for enhancing control strategies without being constrained by outdated or inaccurate models.
Overall, assuming no prior knowledge of disturbances fosters agility and responsiveness in dealing with uncertain conditions prevalent in practical applications while providing robust guarantees based on empirical evidence rather than theoretical conjectures.

How does aligning worst-case noises impact the overall performance and stability of the system

Aligning worst-case noises plays a critical role in shaping the overall performance and stability of a system under uncertainty. When worst-case noises align across different control inputs or scenarios within a given confidence set framework:

Performance Optimization: Aligning worst-case noises ensures consistency when evaluating different control strategies' effectiveness under extreme conditions induced by noise variations. This alignment allows for fair comparisons between different approaches while maximizing performance metrics such as minimizing loss functions associated with noisy dynamics.

Stability Assurance: Consistent worst-case noise alignment provides stability guarantees by establishing boundaries within which controlled variables operate safely despite uncertainties introduced by varying disturbances dependent on decisions made during operation.

Robust Control Design: With aligned worst-case noises guiding decision-making processes regarding robustness measures like confidence sets construction or risk mitigation strategies tailored around these consistent extremes ensures effective management of uncertainties encountered during operations.

In essence, aligning worst-case noises enhances predictability concerning how various factors influence system behavior under adverse conditions while enabling proactive measures aimed at optimizing performance outcomes amidst uncertainty-induced challenges faced during real-world implementations.