Data-Centric Closed Loops

• Data-centric closed loops are iterative frameworks that continuously acquire, process, and update data to enhance control performance and model accuracy.
• They employ active learning and adaptive sampling with feedback mechanisms to maximize sample efficiency and robustness in dynamic environments.
• These systems are applied in autonomous driving, industrial control, and networked systems, offering quantifiable improvements in adaptivity and reliability.

A data-centric closed loop is a control or learning system in which the acquisition, processing, and exploitation of data occur continuously, with system feedback determining both the selection of subsequent data and the adaptation of models or decisions. Data-centric closed loops have become foundational across autonomous systems, AI-driven actuation, and industrial process control. These frameworks explicitly link the real-time state of data acquisition and representation to iterative model or control updates, with the closed loop structured to maximize sample efficiency, adaptivity, and robustness as measured by empirical metrics.

1. Foundational Architecture and Mathematical Formalism

A canonical data-centric closed-loop system comprises the following fundamental stages: data acquisition, representation (embedding or probabilistic modeling), feedback computation, policy or control action selection, and looped update of both dataset and system parameters. In autonomous driving, for instance, the closed-loop pipeline is an iterative mapping $(D_t,\theta_t)\mapsto(D_{t+1},\theta_{t+1})$, where $D_t$ denotes the time-indexed training data distribution (real or synthetic, with explicit focus on hard or rare cases) and $\theta_t$ are model parameters (Li et al., 2024).

In industrial wireless control, sensing data $\mathbf{Y}_i=\mathbf{X}+\mathbf{N}_i$ collected via $k_s$ sensors is transmitted through communication uplinks and downlinks to a control center, where actions $\mathbf{U}_t$ are computed as functions of the best available state estimate. The control loop is tightly coupled with sensing and communication resource constraints (Meng et al., 2023).

General mathematical formulations express the learning or control action via stochastic or deterministic update rules. In data-driven model update:

$$\theta_{t+1} = \theta_t - \eta \,\frac{1}{\sum_i w_i} \sum_{i \in D_t} w_i\,\nabla_{\theta}\ell(f(x_i;\theta_t),y_i)$$

Weights $w_i$ encode the importance of anomalies or corner cases selected adaptively via feedback, while data buffers $D_{t+1}$ incorporate newly collected, synthetic, or mined samples in response to system performance (Li et al., 2024).

2. Data-Driven Control via Closed-Loop Active Learning

A central concern in data-centric closed loops is the design of acquisition policies that ensure dataset informativeness and identifiability of underlying system models. In the setting of unknown linear systems perturbed by bounded disturbances, active learning strategies minimize the volume of the admissible-system ellipsoid $\mathcal{C}(H,\dot{X},\Lambda)$, capturing all matrices $(A,B)$ consistent with data and noise (Feng et al., 2024).

Open-loop active learning seeks input sequences that maximize innovation with respect to current data spans, via distance metrics in the sample matrix $H$. Sample inclusion and weighting (via $\lambda^*$ optimization) are governed by contraction conditions on the ellipsoid volume. In closed-loop, only those feedback-generated data points that strictly shrink the ASE are retained, as proven by non-inferiority of the optimal volume if data are skipped. The recursive inclusion of informative samples guarantees shrinking uncertainty sets and system stability when integrated into tube-based adaptive MPC.

3. Feedback-Governed Dataset Collection and Regulation

Closed-loop feedback control can be extended to the data collection process itself, transforming dataset assembly from a passive pipeline stage into a feedback-regulated, dynamic system (Reis et al., 5 Nov 2025). In the Feedback-Controlled Data Collection (FCDC) paradigm, each incoming data point $x[k]$ is mapped to embedding $z[k]$, and the empirical dataset density is tracked via an online probabilistic model, e.g., Gaussian estimator with parameters $(\mu[k],\Sigma[k])$.

The value function $\psi(z)$ defines the sample's utility regarding redundancy and coverage, leveraging likelihood $\ell(z)$ and Mahalanobis distance $d_M(z)$:

• $$\psi_R(z)=1-\min(1,n[k]/\nu)\exp(-\frac{1}{2}d_M(z)^2)$$ for redundancy reduction;
• $\psi_U(z)=\exp(\frac{1}{2}(d_M^2(z)-r_{\max}^2))$ for uniform target coverage.

Adaptive thresholding ensures dynamic adjustment of acceptance ratios to target sample throughput. Empirical results in vehicle data streams demonstrate 25.9 % improved balance and 39.8 % reduction in storage over baseline open-loop collection. This framework embodies the feedback principle by actively balancing exploration of rare regions and exploitation in dense regions via the shape and schedule of the retention controller.

4. Closed-Loop Data-Enabled Predictive Control and Identification Bias Mitigation

Advanced predictive control in complex dynamical systems leverages closed-loop data to fit input-output sequence models. CL-DeePC (Closed-loop Data-enabled Predictive Control) exploits Hankel matrices and instrumental variables to construct multi-step-ahead predictors that are unbiased even in the presence of noise and closed-loop bias (Dinkla et al., 2024). Offline, block-Hankel matrices $\Psi_{i,s,N}$ and sample covariance fits yield consistent instrumental variable (IV) predictors.

The core optimization is a quadratic program, parameterized entirely by empirical data, that replaces traditional state-space models. CL-DeePC is mathematically equivalent to Closed-loop Subspace Predictive Control (CL-SPC); both are shown to possess superior sample efficiency and noise robustness compared to standard DeePC. The closed-loop learning paradigm avoids asymptotic bias accumulation, maintaining near-oracle performance at dramatically lower sample counts.

5. Embedded Reinforcement Learning and Markov Modeling from Streaming Data

Autonomic closed-loop controllers for systems with streaming and scarce data (e.g., fluid flows, chaotic attractors) can be realized without prior system identification by establishing discrete embedding spaces via locality-sensitive hash functions applied to delayed sensor measurements (Guéniat et al., 2016). The time-embedded sensor vectors $y_t$ are mapped into finite-index Markovian state spaces, over which transition probabilities are empirically estimated.

Policy learning is conducted via online Q-learning, targeting maximization of the discounted sum of expected rewards as determined by physical cost objectives (e.g., drag reduction, energy penalization). The pipeline includes initialization, online ε-greedy action selection, empirical transition model update, and Q-factor iteration. Notably, this framework is robust to noise and capable of dynamical confinement (e.g., Lorenz attractor wing targeting) as well as fluid drag optimization, demonstrating the capacity of pure data-driven closed loops for experimental control law synthesis.

6. Co-Design in Communication-Sensing-Control Networks

In 5G-enabled industrial systems, the closed loop extends across sensing, communication, and control, with each phase's resource allocation and stochastic constraints jointly determining system performance (Meng et al., 2023). Sensor data rates, uplink/downlink capacities, packet loss probabilities, and control law parameters are threaded through Lyapunov stability constraints and quadratic cost function minimization, all within an MPC-inspired co-design optimization.

Trade-offs are explicit: increases in sensor count reduce estimation MSE but can overload uplink bandwidth, while tighter cycle-time constraints demand aggressive delay compensation. Optimizations are solved via interior-point methods; performance metrics are transparently linked to resource budgets. Extensions include multi-agent coordination, hierarchical edge-cloud control, and event-triggered resource activation, all governed by unified data-centric stability and service-level-agreement criteria.

7. Evolution and Taxonomy of Data-Centric Closed-Loop Pipelines

The evolution in autonomous driving closed-loop systems exemplifies milestone shifts:

• Generation 1: batch retraining on static datasets without simulation feedback.
• Generation 2: active-learning with simulation, scenario reprojection, and semi-automatic labeling.
• Generation 3: continuous, online closed-loop learning augmented by generative world models, federated data diversity, and automated map creation (Li et al., 2024).

Empirical metrics—including sample efficiency $E$, model error rate $\varepsilon_t$, and corner-case recall $R_{\text{corner}}$—quantify progress in loop design. Major practical constraints encompass scalability, domain adaptation, CI integration, and annotation quality-speed tension. Future research directions include federated closed-loop learning under privacy restrictions, foundation model deployment for multi-modal data, and hardware-software co-design for real-time inference.

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Data-centric closed loops represent an overview of robust stochastic feedback, adaptive sampling, and real-time learning. By tightly integrating empirical data flow with dynamic control or model update, these frameworks achieve superior sample efficiency, adaptability to real-world nonstationarities, and quantitative guarantees on stability and performance. Recent research highlights their efficacy in autonomous systems, industrial control, and active data assembly, with next-generation extensions incorporating principled co-design, federated learning, and interpretable model feedback.