Online Coreset Selection for Learning Dynamic Systems

TL;DR

This work tackles online data-efficient learning for dynamic systems under bounded disturbances by developing an online coreset selection framework within a set-membership identification (SMI) paradigm. It introduces a stacked polyhedral over-approximation of the feasible-parameter set (FPS) and a threshold-based, geometry-driven coreset trigger that guarantees contraction of uncertainty under persistent excitation, with an explicit bound on the worst-case FPS volume $\mu_{\infty}$ driven by $C(\alpha_0,n_z)$ and the trigger counts. The analysis also yields a Hausdorff-distance bound under disturbance-bound mismatch and an upper bound on the expected coreset size, plus extensions to nonlinear-in-the-parameters models and to noisy measurements, all validated by simulations. The proposed approach provides deterministic, worst-case guarantees for online data reduction in DDC, offering a practical pathway to real-time, data-efficient robust learning and control in dynamic environments.

Abstract

With the increasing availability of streaming data in dynamic systems, a critical challenge in data-driven modeling for control is how to efficiently select informative data to characterize system dynamics. In this work, we develop an online coreset selection method for set-membership identification in the presence of process disturbances, improving data efficiency while preserving convergence guarantees. Specifically, we derive a stacked polyhedral representation that over-approximates the feasible parameter set. Based on this representation, we propose a geometric selection criterion that retains a data point only if it induces a sufficient contraction of the feasible set. Theoretically, the feasible-set volume is shown to converge to zero almost surely under persistently exciting data and a tight disturbance bound. When the disturbance bound is mismatched, an explicit Hausdorff-distance bound is derived to quantify the resulting identification error. In addition, an upper bound on the expected coreset size is established and extensions to nonlinear systems with linear-in-the-parameter structures and to bounded measurement noise are discussed. The effectiveness of the proposed method is demonstrated through comprehensive simulation studies.

Figures (6)

• Figure 1: Schematic diagram of the proposed online learning framework.
• Figure 2: Verification of PE condition in Assumption \ref{['as:PE']}: minimum eigenvalue of the covariance matrix over sliding windows of length $N_u=20$.
• Figure 3: Performance of the threshold-triggered estimator ($\alpha_0 = -0.3$). (a) Evolution of the worst-case volume $\mu_{\infty}(\widehat{\Theta}_k)$. (b) Cumulative number of selected data points.
• Figure 4: Evolution of feasible parameter sets. The top and bottom rows depict the 3D polyhedral uncertainty sets $P^1_k$ and $P^2_k$ at $k = 0$, $k = 20$, and $k = 80$, respectively. Red stars mark the true parameter values.
• Figure 5: Comparison of performance under different threshold parameter $\alpha_0 \in \{-1,-0.5,-0.3,-0.2,0\}$. (a) Evolution of feasible set worst-case volume $\mu_{\infty}(\widehat{\Theta}_k)$. (b) Cumulative number of selected data points under different $\alpha_0$ values. The shaded regions represent the range between the minimum and maximum values.

Theorems & Definitions (46)

• Remark 1
• Proposition 1
• proof
• Remark 2
• Proposition 2
• Remark 3
• Definition 1: Persistent excitation
• Definition 2: Tightness of the bound
• Remark 4
• Lemma 1