Dynamic Probabilistic Assurance (DPA)

• Dynamic Probabilistic Assurance (DPA) is a framework that continuously computes live safety probabilities for complex, stochastic autonomous systems.
• It integrates online monitoring, incremental probabilistic modeling, and Bayesian inference to update risk estimates and trigger timely interventions.
• Empirical applications in autonomous agents, ML-driven safety, and power systems demonstrate reduced risks and enhanced system resilience.

Dynamic Probabilistic Assurance (DPA) is a paradigm and suite of methodologies for providing quantitative, continuously updated probabilistic guarantees regarding the behavior of safety- or mission-critical autonomous systems. It responds to the inadequacy of traditional, static verification and assurance practices in the context of highly complex, stochastic, or learning-enabled components, where unpredictable and emergent behaviors, unbounded state-spaces, or model uncertainties render static proofs insufficient. In DPA, the primary assurance object is no longer whether a catastrophic event can be categorically ruled out, but rather the live probability—with rigorously characterized uncertainty—of the system reaching, avoiding, or remaining within safety- or goal-relevant state sets under all available evidence and runtime observations. The DPA process integrates online monitoring, probabilistic model updating, and dynamic risk quantification, and it produces actionable output for runtime adaptation or intervention.

1. Motivating Principles and Foundational Definitions

Classical approaches to software and system assurance assume deterministic behavior within a bounded, analyzable state-space. However, in agentic AI systems, cyberphysical assets, power systems, and learning-enabled components (LECs), four phenomena routinely undermine these assumptions: (i) stochasticity due to randomization or deep learning outputs, (ii) compounding errors and effective state-space explosion in multi-step tasks, (iii) emergent, context-dependent behaviors not observable in isolation, and (iv) novel failure vectors from adversarial input or control logic (Koohestani, 28 Sep 2025). In this context, traditional assurance seeks answers to the categorical "Will the system fail?", but DPA reframes the question: "With what probability (and within which time/resource bounds) will the system reach, or avoid, a specified set of states?"

Formally, a DPA framework for an agentic, learning-enabled, or safety-critical system is an online process that, at each time step $t$:

• observes traces of the system's input/output and environment;
• incrementally (re)constructs a formal probabilistic model (often a Markov Decision Process, probabilistic automaton, or Bayesian Network);
• evaluates (via probabilistic model checking or Bayesian inference) current probability and expectation bounds for key properties (e.g., reachability of failures, expected time-to-goal);
• issues quantitative assurance metrics and triggers alerts if pre-specified risk thresholds are violated (Koohestani, 28 Sep 2025, Asaadi et al., 2020, Denney et al., 2024).

2. Probabilistic Modeling and Online Learning

At the heart of DPA is the dynamic maintenance and refinement of a probabilistic behavioral model. In agentic AI and autonomous agent settings, this is typically realized as a Markov Decision Process (MDP):

$M_t = (S, A, P_t, R, \gamma)$

where $S$ is a finite set of abstracted states, $A$ a finite set of (high-level) actions, $P_t(s'|s,a)$ the time-indexed, empirical transition probability estimation, $R$ an immediate reward/cost function, and $\gamma$ a discount factor. The model is updated online: every observed transition $(s, a, s')$ increments the corresponding transition count $N_t(s, a, s')$, with $P_{t+1}(s'|s,a)$ recomputed using normalized counts (Koohestani, 28 Sep 2025).

For systems with perception, continuous spaces, or partially observable environments, this modeling may be via particle-filtered probabilistic automata (Cleaveland et al., 2023), Bayesian networks capturing causal links between ML failures, environment, and outcomes (Arshadizadeh et al., 7 Jun 2025), or stochastic dynamic Bayesian networks at the system or component level (Asaadi et al., 2020, Denney et al., 2024).

In learning-enabled contexts, Bayesian uncertainty quantification (e.g., via Gaussian Processes) is also applied to sensor or predictor error distributions, enabling the runtime derivation of confidence intervals and credible bounds for assurance metrics (Asaadi et al., 2023).

3. Risk Quantification and Probabilistic Model Checking

DPA frameworks transform updated models into quantitative risk metrics by applying temporal probabilistic logics or Bayesian queries:

• Probabilistic reachability: determining the maximum (or minimum) probability that the system reaches a target state (e.g., defined by an assurance property $\varphi$) within $k$ steps:

$P_{\max} = ?\ [F^{\leq k} \varphi]$

• Expected cost/reward: computing expected cumulative cost or time to a property:

$E_{\min} = ?\ [C^{\leq k}]$

Model checking is typically performed via tools such as STORM or PRISM, and outputs are compared to thresholds to drive interventions (e.g., run abort, degradation) (Koohestani, 28 Sep 2025, Cleaveland et al., 2023). For Bayesian DPA, system-level failure probabilities are obtained by conditioning causal Bayesian networks on current evidence, with beliefs propagated via conjugate updates (e.g., Beta-Binomial) or forward inference (Arshadizadeh et al., 7 Jun 2025, Denney et al., 2024).

4. Architecture, Instrumentation, and Computational Strategies

A generic DPA architecture comprises:

• Monitoring and event abstraction (observing and mapping system I/O or logs to model-relevant transitions and evidence).
• Online learning/updating of probabilistic models using observed data, leveraging efficient incremental update rules and sliding windows to address non-stationarity (Koohestani, 28 Sep 2025).
• Probabilistic model checking or Bayesian inference (often with periodic recomputation or on-demand depending on computational constraints).
• Assurance reporting and actuation, integrating live assurance metrics with human- or policy-defined intervention logic.

Efficiency is addressed via event filtering (e.g., fast screening to discard obviously secure states (Sabot et al., 2 May 2025)), calibrated surrogate models (machine learning classifiers with probabilistic calibration), and allocation of computational effort to high-risk scenarios, minimizing the need for expensive real-time simulation or model checking (Cremer et al., 2019). Empirically, DPA frameworks achieve overheads ranging from sub-millisecond in particle or Bayesian filters to tens–hundreds of milliseconds for hundreds-state model checkers (Koohestani, 28 Sep 2025, Cleaveland et al., 2023).

5. Applications in Autonomous Agents, Safety-Critical Systems, and Complex Infrastructures

DPA has been instantiated in various domains:

• Agentic AI: AgentGuard applies DPA to LLM-based, tool-using agents, dynamically verifying properties such as success probability, expected number of actions to termination, and probability of deadlock. Empirical gains include 30% reduction in wasted compute and 25% fewer infinite loops compared to static baselines (Koohestani, 28 Sep 2025).
• ML-centric Safety: In vehicle platooning, DPA integrates distribution shift detection (SafeML) with BN-based causal analysis to capture ML-induced failures. Results show 30% reduction in near-collisions versus approaches omitting ML-failure modeling (Arshadizadeh et al., 7 Jun 2025).
• Power Systems: DPA/PDSA combines Monte Carlo simulation catalogues, rigorous statistical error bounds, machine learning screening, and interpretable feature analysis to enable real-time dynamic security assessment, scaling from small (73-bus) to national-scale grids (Sabot et al., 2 May 2025, Cremer et al., 2019).
• Learning-Enabled Components: Dynamic Bayesian Networks and GP-based uncertainty quantification support assurance claims (with live probability and credible intervals) for perception and control modules in autonomous aviation systems (Asaadi et al., 2020, Asaadi et al., 2023, Denney et al., 2024).
• Autonomy and Control: Assurance Monitor Patterns use Bayesian trajectory fusion, dynamic resource allocation, and probabilistic alerting for runtime risk management in navigation and other resource-constrained systems (Duracz et al., 2020).

6. Comparison to Static Assurance and Integration with Assurance Cases

DPA fundamentally departs from static assurance paradigms that rely on design-time arguments, artifact review, or once-off risk assessment. It delivers:

• Timeliness: Assurance metrics adapt instantly to current environmental, behavioral, or evidence shifts.
• Adaptivity: Thresholds can dynamically trigger risk-mitigation logic, reducing hazard exposure under distributional drift, model performance degradation, or unexpected exogenous events (Arshadizadeh et al., 7 Jun 2025, Asaadi et al., 2020).
• Traceability and Quantification: Assurance values are linked to real system operation, with explicit, data-driven rationales, and can be embedded as evidence nodes in dynamic assurance case arguments (e.g., Goal Structuring Notation (GSN) enriched with runtime quantification) (Denney et al., 2024).
• Metric Integration: DPA frameworks express, update, and check explicit metrics (e.g., safety indicators, event frequencies, credible intervals) ensuring quantitative consistency between runtime measurement and assurance claims. Bayesian posterior updates and risk propagation maintain calibration to recent performance and exposure (Denney et al., 2024).

Challenges include guaranteeing the validity/calibration of component models under distribution shift, computational real-time feasibility at scale, requirements for representative data, and regulatory acceptance of live probabilistic assurance evidence (Cleaveland et al., 2023, Asaadi et al., 2020).

7. Empirical Validation, Impact, and Open Research Directions

Published DPA frameworks have demonstrated:

• Improved operational efficiency and risk reduction across agentic AI, power systems, and autonomous vehicles.
• Robustness to rare or shifting conditions by combining MC simulation databases, probability calibration, interpretable machine learning, and principled statistical stopping rules (Sabot et al., 2 May 2025, Koohestani, 28 Sep 2025, Cremer et al., 2019).
• Quantitative linkage between component (LEC) reliability and system-level assurance using closed-form Bayesian updating (Asaadi et al., 2023, Denney et al., 2024).

Current open questions include scalable and adaptive model structure learning, meta-assurance of the quantification models themselves, integration of DPA outputs into certification standards, and the unification of structured assurance claims with probabilistic and runtime evidence pipelines (Asaadi et al., 2020, Denney et al., 2024). Extensions to multi-agent, decentralized systems and richer temporal logic properties are active areas of research (Arshadizadeh et al., 7 Jun 2025).

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Dynamic Probabilistic Assurance establishes a rigorous, data-driven foundation for continuous confidence quantification in complex, adaptive, or learning-enabled systems, unifying runtime statistical inference, formal models, and dynamic assurance case argumentation to directly support automated mitigation, intervention, and visible trust in system operation.