Learning-Augmented Online Allocation under Unreliable Advice: Robustness, Exposure Fairness, and Distribution Shift

Learning-augmented algorithms improve online decisions using predictions, but unreliable advice may harm efficiency and fairness. We study an online allocation problem with finite candidate sets, irreversible decisions, and exposure constraints. We propose a robust and fair rule combining advice with a conservative fallback and fairness correction. Under bounded-error assumptions, we prove consistency and robustness with loss proportional to prediction error. Experiments show stability under adversarial advice and significant reductions in exposure disparity.

Fair Online Resource Allocation

We study the problem of fair online resource allocation, motivated by applications such as refugee resettlement and airline scheduling, where agents arrive sequentially and must be assigned to facilities with limited capacities. We introduce a model that maximizes the overall welfare subject to resource constraints and a Lipschitz fairness requirement, which ensures that similar agents arriving in the same batch receive similar expected outcomes. We first analyze the offline problem, proving that the value of the optimal fair allocation is at least an $Ω(1/γ)$ fraction of the optimal unfair allocation, where $γ$ is the fairness coefficient, thereby bounding the price of fairness. For the online setting, we propose an algorithm based on dual mirror descent that enforces fairness constraints within batches while estimating optimal dual variables. We prove that this algorithm achieves sublinear regret relative to the optimal offline fluid benchmark. Finally, we validate our theoretical results using real-world data from the Refugee Economies Programme, demonstrating the algorithm's performance and examining the trade-offs between welfare maximization and fairness enforcement.

Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making

Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness. However, standard primal--dual methods struggle to update multipliers robustly under stochastic mini-batch feedback, as the noise of mini-batch gradients and constraint estimates can be directly accumulated into the multiplier memory. To address this issue, we propose Residual-Controlled Multiplier Learning (RCML), which reformulates multiplier updating as projected-pressure feedback. The central idea is to decompose the projected multiplier into an effective pressure signal for primal descent and a pressure-memory residual for finite-gain multiplier tracking. To handle heterogeneous and noisy observations, we further augment this residual-integral backbone with modular stochastic stabilization components. For the convex-affine backbone, we establish finite-gain convergence, derive a stochastic residual bound under mini-batch feedback, and show that the residual feedback law admits a local KKT-residual interpretation near regular KKT points of nonconvex problems. Experiments across optimization, allocation, and fair-ranking tasks show that RCML improves feasibility control and multiplier stability while maintaining competitive objective performance. Code is released at https://anonymous.4open.science/r/RCML-3114/.