End-to-End Learning Approach Improves Resource Allocation Under Capacity Constraints

A new paper on arXiv examines how end-to-end policy learning can improve the allocation of scarce resources such as housing assistance and hospital interventions, where decisions must be made immediately and long-run capacity constraints must be respected.

The study, titled “Differentiating Through Dual Prices: End-to-End Policy Learning Under Capacity Constraints,” compares two approaches for learning allocation policies from logged observational data. The research addresses a common real-world problem: systems that must assign resources to people arriving one at a time, with each decision made instantly and long-term usage kept within capacity limits.

Key facts

The baseline approach, described as a decision-blind pipeline, fits one outcome model per treatment using regression, prices each capacitated resource from those models, and assigns each arrival the treatment with the largest predicted outcome minus price. This method, proposed in prior work by Tang et al. (2024), separates the prediction and optimization steps.

The end-to-end approach instead trains outcome models by differentiating an off-policy estimate of the deployed policy’s value through the dual prices themselves. The researchers studied two formulations: an exact nonconvex one and a convex relaxation whose optimum always satisfies capacity constraints in expectation, with explicitly bounded suboptimality.

Every method was evaluated in a queueing simulation to capture the online decision structure. Across six datasets, the two end-to-end variants led the delay-adjusted policy value wherever capacity was scarce, once a waiting period carried even a small cost.

How the methods compare

The decision-blind regression approach predicted ground truth more accurately than the end-to-end methods. However, when resource capacities were stringent, these baselines frequently violated capacity constraints and incurred much longer queueing delays.

The end-to-end training approach proved best suited to settings where resources are genuinely scarce and feasibility matters. The convex relaxation formulation offered the additional advantage of guaranteed constraint satisfaction in expectation, with a known bound on suboptimality.

The research has practical implications for organizations managing scarce resources with capacity limits, including social services, healthcare systems, and any application where delayed decisions carry costs. The findings suggest that optimizing for prediction accuracy alone may lead to policies that fail in practice when capacity constraints bind.

Practical considerations

For AI practitioners and researchers working on resource allocation problems, the study provides a concrete framework for end-to-end training through dual prices. The convex relaxation formulation offers a tractable alternative that maintains theoretical guarantees while improving practical performance over decision-blind approaches.

The evaluation methodology using queueing simulation is notable for capturing the sequential decision structure that real-world allocation systems face. This matters because static evaluation may miss dynamic effects like queueing delays that affect actual system performance.

Limitations and unknowns

The study uses logged observational data, which means the quality of learned policies depends on the data coverage. The methods were evaluated on six datasets, but real-world deployment may reveal additional challenges not captured in simulation.

The convex relaxation guarantees constraint satisfaction only in expectation, not for every individual realization. Organizations with strict per-period capacity limits may need additional safeguards.

The research does not address how these methods perform when the underlying treatment effects change over time, a common occurrence in many social service and healthcare settings.

Source: arXiv cs.LG, “Differentiating Through Dual Prices: End-to-End Policy Learning Under Capacity Constraints” (https://arxiv.org/abs/2608.04669)