Closed-Loop Agentic Systems

• Closed-loop agentic systems are computational architectures characterized by continuous feedback loops integrating perception, planning, action, and verification.
• They utilize specialized modules for reasoning, execution, and introspective verification to ensure error recovery and adaptive learning over long horizons.
• Applications span robotics, security, scientific discovery, and optimization, enforcing strict safety constraints and performance benchmarks.

Closed-loop agentic systems are computational architectures in which agentic components interact with their environment through persistent feedback cycles that couple perception, planning, action selection, execution, and verification phases. These systems are distinguished by their capability to adapt, self-verify, and refine behavior over long horizons, extending beyond static, feed-forward autonomy. Central features include layered modularity, explicit reasoning and goal revision, embedded verification or critic modules, and formal safety constraints, forming a rigorously structured loop that enables robust error detection, recovery, and continual learning (Yang et al., 29 May 2025, Yu, 7 Jul 2025, Miehling et al., 28 Feb 2025).

1. Formal Definitions and Core Loop Architecture

Closed-loop agentic systems are characterized by the continuous cyclical progression through perception ($o_t$), internal state update or belief ($b_t$), planning over adaptive goals ($g_t$), high-level action or plan generation ($\tau_t$), tool invocation, low-level policy execution ($a_t$), and subsequent re-observation ($o_{t+1}$), closing the feedback loop (Yu, 7 Jul 2025). A canonical formalization for such systems is:

• Environment state update: $x_{t+1} = f_{\text{env}}(x_t, a_t)$
• Observation: $o_{t+1} \sim p(o | x_{t+1})$
• Belief update: $b_t = f_b(b_{t-1}, o_t; \theta_{\text{perc}})$
• Goal adaptation: $$g_t = f_{\text{goal}}(g_{t-1}, b_t, u_t^{(\text{hum})})$$
• Agentic planning: $\tau_t = \pi_{\text{agentic}}(b_t, g_t)$
• Tool invocation: $r_t = f_{\text{tool}}(\tau_t; \text{API})$
• Actuation: $$a_t = \pi_{\text{ctrl}}(x_t, \tau_t; \theta_{\text{ctrl}})$$

This cycle instantiated in frameworks such as Agentic Robot enforces explicit stepwise decomposition, real-time execution against sensory input, verifier-gated progression, and recovery on error (Yang et al., 29 May 2025). Modular multi-agent variants, as in MobiLLM, partition the loop into analysis, classification, and actuation agents, each grounding reasoning over external knowledge (Sharma et al., 25 Sep 2025). Multi-agent scientific systems, such as Agentic Discovery, extend the loop across federated agents specializing in distinct phases of scientific workflows within joint Markov decision processes (Pauloski et al., 15 Oct 2025).

2. Component Specialization and Interaction Protocols

Closed-loop agentic systems exhibit explicit specialization:

• Reasoning/Planner modules: Hierarchical decomposition of high-level objectives into subgoals; formalized as $\{t_1, ..., t_N\} = P(T, I_0)$ in robot manipulation (Yang et al., 29 May 2025).
• Executors: Reactive translation of subgoals and real-time observations into low-level control actions, e.g. $a_t = \pi_{\text{exec}}(t_i, O_t)$.
• Verifiers/Critics: Autonomous introspective assessment, periodically gating progression, or triggering recovery actions if completion criteria $\hat{y}_t \in \{\text{Yes}, \text{No}\}$ are not met.
• Tool Use Agents: Invocation of external APIs for knowledge retrieval, protocol execution, or environmental manipulation, often grounded in domain knowledge bases (e.g., MITRE FiGHT, ChemAtlas KG).

Interaction protocols are governed by structured hand-off rules, buffer management, recurrent verification scheduling, and recovery or escalation policies (e.g., capped retries, human-in-the-loop override) (Yang et al., 29 May 2025, Sharma et al., 25 Sep 2025). Asynchronous message passing and actor-style agent interfaces enable distributed orchestration in multi-agent agentic discovery platforms (Pauloski et al., 15 Oct 2025).

3. Feedback, Emergent Cognition, and Adaptation

Functional agency is established by systems that generate actions toward objectives, represent outcomes, and adapt when mappings shift (Miehling et al., 28 Feb 2025). Closed-loop feedback enables mechanisms for higher-order cognition:

• Embodied cognition: Multimodal feedback integrating visual, tactile, and motor signals fosters generalized abstraction.
• Predictive processing: Top-down generative models predict sensory input; prediction errors are minimized through perceptual inference or active manipulation, guiding causal model construction.
• Metacognition: Agents track internal confidence and discrepancies, broadcasting uncertainty estimates, pooling agent-level confidence via inter-agent protocols, and triggering reflective adaptation.

Emergent causal reasoning parallels the interventionist view: agents alternate estimation of $P(\text{outcome}|\text{action})$ with active sampling; prediction errors signal interventions, refining structural causal models. In closed-loop security agents, iterative recon–exploit–RCA–patch–validate chains support robust, self-correcting diagnosis and remediation (Khurana et al., 2 Oct 2025).

4. Safety, Verification, and Performance Measurement

Closed-loop architectures incorporate explicit safety, efficiency, and correctness constraints throughout the loop:

• Safety barrier constraints: $h_i(x_{t+1}) - h_i(x_t) \geq -\kappa h_i(x_t)$ ensure system operates within safe regions (Yu, 7 Jul 2025).
• Latency and real-time bounds: $L_{\text{loop}} \leq L_{\text{max}}$, guaranteeing bounded reaction times.
• Ethical and regulatory alignment: Constraints and overrides (e.g., $E[\text{ethical_violation}(b_t, a_t)] \leq \epsilon$) enforce compliance.
• Capability benchmarking: The CLASP framework and Closed-Loop Capability (CLC) Score operationalize agentic efficacy (correctness, rate, cycle efficiency) and efficiency (parsimony across planning, tool use, memory, reasoning, reflection, perception) (Khurana et al., 2 Oct 2025).

Performance metrics are domain-specific: manipulation success rate (Agentic Robot: 79.6% on LIBERO), remediation validity and response latency (MobiLLM), code speedup (ComPilot: 2.66×–3.54× best-of-5 runs) (Merouani et al., 1 Nov 2025, Yang et al., 29 May 2025, Sharma et al., 25 Sep 2025). Cross-agent discovery throughput scales nearly linearly with federated HPC resources (Pauloski et al., 15 Oct 2025).

5. Domain-Specific Instantiations

Closed-loop agentic principles are realized across diverse application domains:

• Robotics: Agentic Robot implements Standardized Action Procedure (SAP), marrying reasoning, subgoal decomposition, execution, and introspective verification in long-horizon manipulation (Yang et al., 29 May 2025).
• Mobility and Vehicles: Agentic vehicles integrate high-level cognitive layers, dynamic goal adaptation, and contextual communication, contrasted with feed-forward autonomous vehicles (Yu, 7 Jul 2025).
• Security: MobiLLM and closed-loop security agents autonomously analyze, classify, and mitigate threats using modular multi-agent LLM frameworks with operator guardrails and retrieval-anchored reasoning (Sharma et al., 25 Sep 2025, Khurana et al., 2 Oct 2025).
• Scientific Discovery: Agentic Discovery orchestrates cooperative agents aligned with research workflow stages, featuring self-describing interfaces, federated orchestration, and closed-loop joint-policy optimization (Pauloski et al., 15 Oct 2025).
• Code Optimization: Agentic Auto-Scheduling leverages general-purpose LLMs dialoguing with compilers in iterative feedback loops to auto-tune loop nests, outperforming state-of-the-art optimizers when feedback is enforced (Merouani et al., 1 Nov 2025).
• Process Design: AutoChemSchematic AI deploys SLMs, graph RAG, simulator-in-the-loop fitness checks, and advanced optimization for automated generation and validation of chemical process flowsheets and instrumentation diagrams (Srinivas et al., 30 May 2025).

6. Research Challenges and Future Directions

Open challenges identified across works include:

• Scaling memory and introspection: Most systems exhibit episodic rather than longitudinal memory, limiting cumulative learning (Khurana et al., 2 Oct 2025).
• Inter-agent competence transfer and delegation: Trust quantification and cold start adaptation remain open problems in multi-agent deployment (Miehling et al., 28 Feb 2025).
• Subgoal chain control: Automated monitoring and human-in-the-loop escalation are required to constrain autonomously emergent subgoal hierarchies at machine speed.
• Sim-to-real transfer and robustness: Particularly in embodied tasks, verifier resilience under domain shift, lighting, or occlusions is critical (Yang et al., 29 May 2025).
• Policy enforcement and interpretability: Across federated systems and regulatory environments, the need for explainable introspection traces and reproducible provenance is emphasized (Pauloski et al., 15 Oct 2025).
• Efficiency and parsimony: The CLC Score penalizes capability overuse, guiding agent development toward minimal sufficient resource allocation (Khurana et al., 2 Oct 2025).

A plausible implication is that further progress in closed-loop agentic systems depends on harmonizing rigorous architectural modularity, safety-critical loop design, domain-specific adaptation, and scalable, transparent benchmarking methodologies.

7. Summary Table: Core Agentic Loop Elements Across Domains

Domain/Application	Loop Phases	Key Specializations
Robot Manipulation	Perception → Planning → Execution → Verify	SAP: LLM planner, VLA executor, verifier (Yang et al., 29 May 2025)
Mobility Systems	Observe → Reason → Goal Adapt → Plan → Act	Cognitive/communicative layers, tool use (Yu, 7 Jul 2025)
Security (6G O-RAN)	Sense → Analyze → Classify → Plan → Actuate → Feedback	Modular LLM agents, KB grounding, human escalation (Sharma et al., 25 Sep 2025)
Code Optimization	Propose → Compile → Measure → Refine	Compiler-in-loop, agent-compiler feedback (Merouani et al., 1 Nov 2025)
Scientific Discovery	Observe → Hypothesize → Experiment → Analyze → Update	Federated agents spanning method phases (Pauloski et al., 15 Oct 2025)

Closed-loop agentic systems thus encompass a spectrum of architectures unifying feedback-centric planning, verified action execution, robust adaptation, and introspective capabilities, enabling reliable, explainable, and high-performance artificial agency across diverse applications.