1 Introduction↩︎

Artificial intelligence (AI) systems have moved rapidly from research prototypes into production environments, transforming sectors such as healthcare, agriculture, industrial automation, and autonomous systems [1]. The most recent wave of generative-AI and large language models has accelerated this trend by setting new standards in language understanding, content generation, and decision support [2], enabling applications that range from automated customer interaction to advanced research assistants [3].

Despite this momentum, AI systems deployed in the field exhibit a recurring set of weaknesses. Their internal representations remain opaque and only marginally interpretable, which limits trust in real-time autonomous decision-making [4]. They are sensitive to demographic and statistical biases inherited from training data, which can amplify societal disparities and produce unstable behaviour at the population level [5]. Standard training pipelines do not protect against catastrophic forgetting under sequential or non-stationary tasks [6], and the resulting models remain vulnerable to adversarial and out-of-distribution perturbations [7].

These weaknesses are amplified by the operating environments in which contemporary AI systems are actually deployed. Edge, federated, and distributed settings impose tight computational, networking, and energy constraints [8], while real-time autonomous deployments demand safety guarantees that conventional learning algorithms do not natively provide [9]. Under such conditions, different AI models may exhibit very different trade-offs across predictive accuracy, fairness, robustness, latency, and interpretability. Conventional static resource-allocation strategies cannot adapt to evolving workloads, demographic shifts, or unexpected disturbances, and therefore degrade both efficiency and operational reliability [10].

A growing body of evidence therefore points to the need for adaptive resource orchestration frameworks that continuously reallocate computational budget across a population of heterogeneous AI models in response to their evolving utility, resilience, and human-centric behaviour. To be useful in practice, the orchestration policy must be (i) closed-loop, so that the controller reacts before performance has degraded; (ii) stability-aware, so that bounded disturbances do not destabilise the global system; and (iii) human-centric, so that fairness and interpretability are treated as first-class quantities rather than as post-hoc constraints.

The primary contribution of this work is AURORA-AI, a Hamilton-Jacobi-Bellman feedback orchestration policy that unifies Lyapunov-based stability guarantees with a fairness-aware composite utility, enabling closed-loop redistribution of computational budget across heterogeneous AI models operating under non-stationary, human-centric deployment conditions. This primary contribution is supported by three subsidiary developments :

• a fairness-aware composite utility function that jointly captures predictive performance, demographic parity, cost, latency, robustness, and human-centric model characteristics;

• a stress-rich simulation environment that concurrently injects demographic bias shocks, gradual concept drift, and abrupt black-swan disruptions in order to exercise every analytical component of the proposed framework;

• a resilience-oriented evaluation methodology grounded in \(\alpha\)-quantile, super-quantile, recovery time, and Lyapunov-inspired stability metrics, which together quantify both average and worst-case behaviour under disruption.

2 Methodology↩︎

Let us consider the parameter vector \(\boldsymbol{\theta}(t)\in\mathbb{R}^d\). Its evolution follows the gradient flow \[\dot{\boldsymbol{\theta}}(t)=-\eta(t)\nabla_{\boldsymbol{\theta}} \mathcal{L}\bigl(\boldsymbol{\theta}(t),\mathbf{x}(t)\bigr),\] with loss function \(\mathcal{L}\) and adaptive learning rate \(\eta(t)>0\).

Let us define the Lyapunov function \[\label{eq:lyap} V(\boldsymbol{\theta},t)=\tfrac12\,\boldsymbol{\theta}^{\top} \mathbf{P}(t)\,\boldsymbol{\theta},\qquad \mathbf{P}(t)\succ 0.\tag{1}\] When \(\dot{V}(\boldsymbol{\theta},t)<0\;\;\forall\,\boldsymbol{\theta} \neq\boldsymbol{\theta}^{*}\), the equilibrium \(\boldsymbol{\theta}^{*}\) is asymptotically unique. The real parts of the eigenvalues of the linearised system \(\dot{\boldsymbol{\theta}} =\mathbf{A}(t)\boldsymbol{\theta}\) should be uniformly strictly negative.

In order to handle forgetting, the loss is augmented using a quadratic penalty \[\label{eq:ewc} \mathcal{L}_{\mathrm{EWC}}(\boldsymbol{\theta}) =\mathcal{L}_{\mathrm{task}}(\boldsymbol{\theta}) +\frac{\lambda}{2}\sum_{i}F_{i}\bigl(\theta_{i}-\theta_{i}^{*}\bigr)^{2},\tag{2}\] with learned parameters \(\theta_{i}^{*}\) and diagonal entry \(F_{i}\) of the Fisher information matrix [6] \[F_{i}=\mathop{\mathrm{\mathbb{E}}}_{\mathbf{x}\sim\mathcal{D}_{\mathrm{old}}}\!\left[\left( \frac{\partial\log p(\mathbf{x}\mid\boldsymbol{\theta})}{\partial \theta_{i}}\right)^{2}\right].\] If the log-likelihood \(\ell(\boldsymbol{\theta})=\log p(\mathbf{x}\mid\boldsymbol{\theta})\) is \(\mathcal{C}^{2}\), then the approximation becomes valid in a neighbourhood of the optimum with empirical Fisher matrix \[\hat{\mathbf{F}}(\boldsymbol{\theta})=\frac{1}{n}\sum_{i=1}^{n}\nabla \ell(\boldsymbol{\theta};\mathbf{x}_{i})\nabla\ell(\boldsymbol{\theta}; \mathbf{x}_{i})^{\top}\] being positive definite (\(\hat{\mathbf{F}}(\boldsymbol{\theta}) \succ 0\)).

We model resource allocation with a continuous-time Markov chain over a finite state space \(\mathcal{S}=\{1,\dots,M\}\). The system state \(s\in\mathcal{S}\) represents the resource level with the vector \(\mathbf{R}\in\mathbb{R}_{\ge 0}^{N}\) and the performance score with the vector \(\mathbf{P}\in[0,1]^{N}\) separated into distinct measurement intervals. The resource available to agent \(k\) at time \(t\) equals \(R_{k}(t)\) while its performance at the same time equals \(P_{k}(t)\), calculated using an exponentially weighted moving average through previous rewards \[P_{k}(t)=\int_{0}^{t}e^{-\rho(t-\tau)}\bigl(1-\mathcal{L}_{k}( \boldsymbol{\theta}_{k}(\tau))\bigr)\,d\tau.\]

The chain jumps from state \(i\) to state \(j\) at rate \(q_{ij}(\mathbf{a})\) which depends on the selected action vector \(\mathbf{a}\). The transition rates establish that \(q_{ij}(\mathbf{a})\) must remain non-negative for all cases where \(i\ne j\) and the probability of staying in state \(i\) equals the negative sum of all probabilities that transition to different states.

Let the compact action space be represented by the set \(\mathcal{A}\). The optimal policy \(\pi^{*}:\mathcal{S}\to\mathcal{A}\) is defined by \[\pi^{*}=\arg\max_{\pi}J(\pi),\] \[J(\pi)=\mathop{\mathrm{\mathbb{E}}}\!\left[\int_{0}^{\infty}e^{-\omega t}\sum_{k=1}^{N}\bigl( \alpha P_{k}(t)-\mu R_{k}(t)\bigr)\,dt\;\middle|\;\pi\right],\] with \(\omega>0\) the discount rate.

The resource dynamics of each agent \(k\) are controlled by the Itô stochastic differential equation \[\label{eq:sde} dR_{k}(t)=\bigl(-\lambda R_{k}(t)+\beta P_{k}(t)\bigr)\,dt +\sigma\,dW_{k}(t),\qquad \lambda,\beta,\sigma>0,\tag{3}\] which uses independent standard Wiener processes \(\{W_{k}(t)\}_{t\ge 0}\) that describe continuous processes starting at zero (\(W_{k}(0)=0\)) and exhibit a Gaussian distribution for the time interval between any two points in time. This process represents zero-mean Gaussian white noise because it produces noise with covariance structure \(\mathop{\mathrm{\mathbb{E}}}[\dot{W}_{k}(t)\dot{W}_{k}(\tau)]=\delta(t-\tau)\), which results in unpredictable changes to resource levels.

The value function \(V(\mathbf{R},\mathbf{P})=\max_{\pi}J(\pi)\) obeys the Hamilton-Jacobi-Bellman (HJB) equation, by virtue of the dynamic programming principle and Itô’s lemma as proven in : \[\label{eq:hjb} \omega V=\max_{a\in\mathcal{A}}\left(\sum_{k}\bigl(\alpha P_{k}- \mu R_{k}\bigr)+\mathcal{L}_{a}V\right),\tag{4}\] with \(\mathcal{L}_{a}\) the infinitesimal generator of the controlled diffusion. This defines the relationship between the value function \(V\) and the action space which contains all elements \(a\) from set \(\mathcal{A}\). The HJB equation establishes complete optimality requirements because it produces the most suitable feedback mechanism for solving control problems unlike open-loop control methods.

If the state space \(\mathcal{S}\subset\mathbb{R}_{\ge 0}^{N}\times [0,1]^{N}\) is compact and the transition coefficients are continuous, then the Bellman optimality equation admits a unique solution \(V\), and a stationary optimal policy \(\pi^{*}\) (measurable in the state) exists.

The fairness component measures the violation of equalised odds through the calculation of positive prediction-rate differences between the two demographic groups \(D=1\) and \(D=0\). The bias-decay law \[\label{eq:bias} \dot{b}(t)=-\kappa\,b(t)+\nu\sum_{i}w_{i}(t)\frac{\partial \mathcal{L}_{\mathrm{fair}}}{\partial\theta_{i}},\qquad \kappa>0,\tag{5}\] describes how the bias term changes over time. The equilibrium state \(b=0\) is asymptotically stable provided \(\kappa>\nu\max_{i}|w_{i}|\,\|\partial^{2} \mathcal{L}_{\mathrm{fair}}/\partial\theta_{i}\partial b\|\). The constant \(\kappa\) acts as the rate of exponential bias-leakage decay in the linearised system \(\dot{b}=-\kappa b\).

The loss function \(\mathcal{L}(\boldsymbol{\theta})\) demonstrates coercive behaviour : the loss tends to infinite values as the input variable diverges. The empirical Fisher matrix is positive semi-definite by construction, but it becomes singular when its rank drops below requirement, either because of under-parameterised models or insufficient data. Newton-type updates require inversion, which is prevented by singularity in the formula \(\boldsymbol{\theta}\leftarrow\boldsymbol{\theta}-\eta \hat{\mathbf{F}}^{-1}\nabla\mathcal{L}\) used by natural gradient descent to handle curvature. We apply a Tikhonov regulariser \(\hat{\mathbf{F}}_{\epsilon}=\hat{\mathbf{F}}+\epsilon\mathbf{I}\) (\(\epsilon>0\)) to restore invertibility, since this method creates a positive-definite matrix \(\hat{\mathbf{F}}_{\epsilon}\succ 0\) which stabilises updates.

The continuous-time Markov decision process satisfies the drift condition \(\mathop{\mathrm{\mathbb{E}}}[\Delta V]\le -c\|(\mathbf{R},\mathbf{P})\|+d\) for a suitable Lyapunov function \(V\), a positive constant \(c\), and a finite constant \(d\). The proof demonstrates geometric ergodicity through the transition kernel which reaches its stationary distribution at an exponential rate, thus showing that infinite-horizon reward calculation remains constant regardless of starting conditions.

The super-quantile measure, which characterises black-swan (extreme) performance shocks, is defined as \[\label{eq:superq} \bar{q}_{\alpha}=\frac{1}{1-\alpha}\int_{\alpha}^{1}q_{X}(\beta)\,d\beta,\tag{6}\] which organisations should use to decrease their tail risk. The Lyapunov condition \(\dot{V}<0\) guarantees stability under bounded perturbations, while the drift condition ensures ergodicity and recovery. The simulations of Section 3 will show that the system penalises unfair conduct while achieving recovery from major disruptions and decreasing tail risk, which results in higher stability compared to the static baseline that violates the condition \(\dot{V}<0\).

3 Numerical Results and Discussion↩︎

This section evaluates the AURORA-AI framework in a discrete-time, non-stationary deployment environment that is purposely engineered to stress every analytical claim of Section 2. In particular, the simulation probes (i) the Lyapunov stability condition \(\dot{V}(\boldsymbol{\theta},t)<0\) associated with Eq. (1 ), (ii) the HJB-derived feedback policy \(\pi^{*}\) of Eq. (4 ), (iii) the elastic-weight penalty \(\mathcal{L}_{\mathrm{EWC}}\) in Eq. (2 ), (iv) the bias-decay law in Eq. (5 ), and (v) the super-quantile tail-risk measure \(\bar{q}_{\alpha}\) in Eq. (6 ). The same environment serves as the empirical instantiation of the third contribution stated in Section 1.

3.1 Simulation Environment and Stressors↩︎

The environment hosts \(N=5\) heterogeneous AI models that differ in predictive accuracy, fairness, robustness, latency, cost, and interpretability. Each episode runs for \(T=350\) time steps with \(500\) samples per step. Three concurrent stressors are injected to exercise distinct components of the framework : a) a demographic bias shock active over \(t\!\in\![120,190]\) that drives the parity gap upward and stresses the bias-decay law of Eq. (5 ); b) gradual concept drift that perturbs the empirical loss landscape and exercises the Fisher-weighted penalty \(\mathcal{L}_{\mathrm{EWC}}\) of Eq. (2 ); c) an abrupt black-swan degradation at \(t=160\) which crashes the global performance and probes both the super-quantile estimator and the Lyapunov-recovery argument.

To position AURORA-AI within the broader literature, five controllers are compared against the proposed framework : an equal-allocation Static baseline, classical Round-Robin, a pure-exploitation Greedy best-arm policy, a LinUCB contextual bandit [11], and a deep reinforcement-learning agent based on PPO [12]. All controllers act on the same compact action space \(\mathcal{A}\) introduced in Section 2. Performance is reported using mean global performance, \(\alpha\)-quantile, super-quantile \(\bar{q}_{\alpha}\), mean and maximum demographic parity gap, recovery time (defined as the smallest \(\Delta t\) such that performance returns within \(2\%\) of the pre-shock plateau), the percentage of stable steps (steps for which \(\Delta V<0\)), and a human-centric explainability score. Aggregated single-run results are summarized in Table 1.

3.2 Performance Resilience and Black-Swan Recovery↩︎

Fig. 2 reports the temporal evolution of the global system performance for AURORA-AI and the Static baseline. Before the disruption, both controllers converge to an indistinguishable plateau near \(0.92\), confirming that under nominal conditions both strategies extract a comparable utility from the resource budget. At \(t=160\) the black-swan event drives both systems below \(0.55\). AURORA-AI then exhibits the signature bounce-dip-climb trajectory predicted by the HJB feedback policy of Eq. (4 ) : an initial fast bounce as the controller redirects budget toward Lyapunov-stable models, a controlled dip near the \(\alpha\)-quantile while the dynamic equilibrium is re-established, and a smooth climb back to the pre-shock plateau. The Static baseline, which has no feedback channel, relaxes only through the slow exponential dynamics of the SDE in Eq. (3 ) and requires \(88\) time steps to recover, whereas AURORA-AI achieves recovery within the resolution of one time step.

The two horizontal references in Fig. 2 mark the \(\alpha\)-quantile (\(0.7666\)) and super-quantile \(\bar{q}_{\alpha}\) (\(0.6729\)) attained by AURORA-AI. They are lifted by \(29.0\%\) and \(25.1\%\) relative to the Static baseline. This empirical lift is the direct signature of the tail-risk inequality implied by Eq. (6 ) : redistributing budget toward Lyapunov-stable arms shrinks the lower tail of the performance distribution. The closed-loop system behaves like a damped feedback oscillator : the strict negative-definiteness of \(\dot{V}\) ensures rapid dissipation of post-shock perturbation energy, while the discounted reward in \(J(\pi)\) penalises any prolonged degradation. The two effects jointly produce the observed fast-recovery profile and validate the first contribution claimed in Section 1.

3.3 Comparison with State-of-the-Art Controllers↩︎

To rule out the possibility that AURORA-AI is competitive only against a non-adaptive reference, the same disruption was replayed under five established controllers. Fig. 3 overlays the performance trajectories. Static and Round-Robin recover only by \(t\!\approx\!250\); Greedy is the noisiest because pure exploitation chases an unstable arm; LinUCB sits in the middle, limited by its linear context model under non-stationarity; PPO is the strongest baseline, recovering in approximately \(22\) steps. AURORA-AI is the only method that achieves near-instantaneous response together with the highest asymptotic plateau, which is consistent with the Pareto-optimality that the HJB equation guarantees over the full action space \(\mathcal{A}\). Bandit and pure-RL controllers optimise a scalar reward and are therefore blind to the geometry of \(V(\boldsymbol{\theta},t)\) : they react to the shock only after it has propagated into the reward signal. AURORA-AI exploits the Lyapunov gradient directly, so the corrective action is applied while the perturbation is still being absorbed by the SDE dynamics of Eq. (3 ). This is why the proposed controller shifts the recovery curve to the left of every baseline.

3.4 Tail-Risk Distribution↩︎

Fig. 4 reports the empirical histogram of the per-step performance for AURORA-AI together with the \(\alpha\)-quantile and super-quantile reference lines. The probability mass is concentrated above the \(\alpha\)-quantile, with only a thin lower tail that survives the black-swan event. This is the empirical analogue of the inequality \(\bar{q}_{\alpha}\!\geq\! q_{\alpha}\) implied by Eq. (6 ) : when the lower tail is short, the super-quantile lies close to the \(\alpha\)-quantile, signalling a light-tailed regime. The closed-loop combination of Eqs. (4 ) and (1 ) acts as a contraction on the state space. Trajectories that stray into the lower tail are pulled back toward the equilibrium \(\boldsymbol{\theta}^{*}\) at an exponential rate, hence the visibly truncated lower tail. This realises the resilience-oriented evaluation listed as the fourth contribution in Section 1.

3.5 Dynamic Resource Allocation↩︎

Fig. 5 traces the resource share assigned by AURORA-AI to each of the five heterogeneous models. Three regimes are visible : (i) a near-balanced regime during the nominal phase, in which the budget is distributed uniformly among the four interpretable models while the unstable Model \(1\) is gradually de-funded as the bias-shock amplifies its parity gap; (ii) an emergency regime triggered by the black-swan event, in which the controller reroutes most of the budget to the most Lyapunov-stable arm (Model \(2\)); (iii) a re-balancing regime in which Models \(3\), \(4\) and \(5\) are progressively re-funded as their performance scores stabilize. The reallocation pattern is the Markov-decision-process analogue of an emergency vasoconstriction response : when one path becomes unsafe, the budget is rerouted to the path that minimises the variance of the closed-loop trajectory, exactly as prescribed by the optimisation of \(J(\pi)\) in Section 2. The de-funding of Model \(1\) before the disruption demonstrates the predictive power of the controller : the bias-shock already breaches the constant \(\kappa\) in Eq. (5 ) for that arm, and the orchestrator anticipates the failure rather than reacting to it. This validates the second contribution of Section 1.

3.6 Lyapunov Energy and Stability Analysis↩︎

Figs. 6 and 7 report the Lyapunov-inspired energy function \(V(\boldsymbol{\theta},t)\) and its discrete time derivative \(\Delta V\). Pre-shock both controllers maintain \(V\) below a small constant level. After the black-swan event \(V\) spikes to \(\approx0.04\) for both systems but the AURORA-AI energy collapses back within \(\approx20\) steps, whereas the Static energy relaxes only over \(\approx70\) steps. The corresponding \(\Delta V\) trace shows that AURORA-AI produces a deeper negative excursion right after the spike, i.e. it dissipates the post-shock energy more aggressively. The percentage of steps for which \(\Delta V<0\) rises from \(43.27\%\) (Static) to \(46.99\%\) (AURORA-AI), thereby satisfying the Lyapunov stability condition over a larger fraction of the horizon. The Lyapunov function plays the role of a thermodynamic free-energy : the shock injects free-energy into the system and the controller acts as a heat-bath that absorbs it. AURORA-AI couples to this bath through the HJB feedback channel of Eq. (4 ), which explains both the faster decay of \(V\) and the larger fraction of negative \(\Delta V\) steps. This empirically verifies the stability claim made in Section 2.

3.7 Human-Centric Explainability↩︎

Fig. 8 reports the explainability score, defined as the budget-weighted average of the per-model interpretability indices. The Static baseline yields a flat \(0.7040\) since its allocation never changes; AURORA-AI maintains a higher score throughout the episode, including a transient drop during the recovery transient when the budget is concentrated on the most performant (and slightly less interpretable) Model \(2\). The mean score increases from \(0.7040\) to \(0.7442\) (\(+5.7\%\)). Because \(\pi^{*}\) optimises the composite utility introduced in Section 2, interpretability is treated as a first-class quantity rather than as a secondary constraint. The controller therefore exploits the post-recovery slack to re-fund interpretable models without sacrificing performance, in agreement with the human-centric design objective listed as the second contribution in Section 1.

4 Conclusion↩︎

This paper introduced AURORA-AI, an adaptive utility-driven resource orchestration framework that unifies Hamilton-Jacobi-Bellman feedback control, Lyapunov-based stability monitoring, and a fairness-aware composite utility into a single closed-loop policy for resilient human-centric AI deployment under non-stationary conditions. The proposed framework was evaluated in a stress-rich discrete-time simulation that concurrently injects demographic bias shocks, gradual concept drift, and abrupt black-swan disruptions, and was compared against five established controllers : Static, Round-Robin, Greedy, LinUCB, and a deep reinforcement-learning agent based on Proximal Policy Optimisation. The empirical evidence reported in Section 3 confirms that every theoretical object introduced in Section 2 – the Lyapunov function in Eq. (1 ), the HJB feedback policy in Eq. (4 ), the elastic-weight penalty of Eq. (2 ), the bias-decay law of Eq. (5 ), and the super-quantile risk measure of Eq. (6 ) – has a measurable counterpart that improves over the strongest baseline. AURORA-AI achieves immediate recovery from the black-swan disruption against \(88\) time steps for the Static baseline and \(22\) for PPO, lifts the \(\alpha\)-quantile and the super-quantile by \(29.0\%\) and \(25.1\%\) respectively, simultaneously reduces both mean and maximum demographic parity gap, and increases the fraction of Lyapunov-stable operating steps from \(43.27\%\) to \(46.99\%\). Beyond the quantitative improvements, the manuscript establishes a methodological loop in which each result is traceable back to a specific equation of the framework and to a stated contribution of the introduction, providing a self-consistent basis for future extensions.

Three directions are particularly promising for future work. First, the closed-loop policy can be generalised to a fully decentralised multi-agent setting in which several orchestrators negotiate local resource budgets while preserving global Lyapunov stability. Second, the fairness-aware utility function can be enriched with additional human-centric axes such as carbon footprint, energy efficiency, and on-device privacy budgets, broadening the scope of the optimisation. Third, the simulation-based validation can be transferred to a hardware-in-the-loop testbed in order to characterise the interaction between the HJB feedback law and real-world latency, jitter, and packet-loss profiles. Each of these extensions builds directly on the closed-loop architecture introduced in this work and inherits its stability and tail-risk guarantees.

Acknowledgment↩︎

This work is supported by HORIZON-HLTH-2024-ENVHLTH-02-06 project ENACT under Grant Number 101157151.

References↩︎