Computable Fairness: Boltzmann-Softmax Control for AI Resource Allocation

Modern AI systems are increasingly deployed under non-stationary computational, demographic, and operational conditions in which static resource allocation strategies degrade both predictive performance and human-centric properties such as fairness and explainability. This paper presents AURORA-AI, an Adaptive Utility-driven Resource Orchestration framework for Resilient AI that unifies Hamilton-Jacobi-Bellman feedback control, Lyapunov-based stability monitoring, and a fairness-aware composite utility into a single closed-loop policy.The framework continuously redistributes computational budget across a population of heterogeneous AI models so that the global utility, defined jointly over predictive performance, demographic parity, cost, latency, robustness, and interpretability, remains maximised under disruption. The framework is evaluated in a stress-rich discrete-time simulation that concurrently injects demographic bias shocks, gradual concept drift, and abrupt black-swan disruptions, and is compared against five established controllers including Static, Round Robin, Greedy, LinUCB, and a deep reinforcement-learning agent based on Proximal Policy Optimisation. AURORA-AI achieves immediate recovery from the black-swan event compared to eighty-eight time steps for the Static baseline and twenty-two for Proximal Policy Optimisation, lifts the alpha-quantile and the super-quantile by twenty-nine and twenty-five percent respectively, simultaneously reduces the mean and maximum demographic parity gap, and increases the fraction of Lyapunov-stable operating steps. These results indicate that fairness-aware adaptive orchestration grounded in stability theory is a practical and theoretically motivated path toward resilient human-centric AI deployment.

Resource allocation across multiple agent groups arises in many applications including e-commerce recommendation systems, housing assignment, and course allocation, and is commonly formulated as an optimization problem with diversity constraints to ensure group fairness. Existing approaches typically enforce these constraints as hard conditions, which overly restrict the feasible solution space and often lead to suboptimal allocations. In this paper, we propose PRA, a parameterized framework for fair resource allocation under diversity constraints. Inspired by the use of risk-aversion parameters in economic models, PRA introduces a set of controllable inequality-aversion parameters to softly regulate group-level diversity, thereby enabling flexible trade-offs between fairness and allocation efficiency. With appropriately calibrated parameters, PRA yields fairness-optimal assignments that comply with the specified diversity constraints. To accommodate additional application-specific constraints, we further extend the framework to an adaptive variant, APRA. We establish that the optimality of both PRA and APRA holds regardless of the chosen fairness metric and the nature of the additional constraints, underscoring the generality and robustness of our approach. Extensive experiments on three real-world applications demonstrate that our proposed framework consistently outperforms existing baselines in both effectiveness and robustness.

Dynamic multi-resource allocation is a central problem in shared computing environments, where users' demands arrive sequentially and resources must be distributed fairly without knowledge of future demands. Existing methods emphasize fairness guarantees such as Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, but often overlook system utility. Moreover, these fairness criteria are mutually incompatible, preventing strict enforcement of them at the same time. We propose a neural allocation mechanism that reconciles fairness with utility through multi-objective optimization during sequential rollout. We first formalize fairness in the dynamic setting via stepwise loss functions for Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, enabling differentiable training. Leveraging non-wastefulness, we parameterized the solutions by constraining allocations to the subspace of demand while allowing elastic over-allocation when resources remain available. Empirical results demonstrate that our learned allocator achieves substantially higher utility at comparable levels of fairness, uncovering clear Pareto-frontier-like tradeoffs across metrics.