Constrained Learning-to-Rank for Controlled Trade-offs in Multi-Objective Ranking Systems

Learning-to-rank is a fundamental problem in computer science, with wide applications in information retrieval, recommender systems, and online decision-making. In many realworld settings, ranking models must simultaneously optimize multiple competing objectives while maintaining explicit control over model behavior. Existing approaches typically rely on scalarization or implicit multi-objective learning, which lack formal mechanisms to enforce constraint satisfaction and often require extensive manual tuning. In this paper, we propose CLTR (Constrained Learning-to-Rank), a general framework that formulates learning-to-rank as a constrained optimization problem, where a primary utility objective is maximized subject to an explicit constraint on a secondary ranking metric. The framework is instantiated via an augmented Lagrangian method with adaptive dual-variable updates, enabling stable training dynamics and direct control over constraint satisfaction. CLTR can be seamlessly integrated into both gradient-boosted and neural ranking models with minimal modification. We evaluate the proposed approach on standard learning-to-rank benchmarks (MSLR-WEB10K and Istella-S) under a controlled multiobjective setting. Experimental results show that CLTR achieves high levels of constraint satisfaction (over 93% at the query level) while consistently improving the primary objective compared to scalarization-based and multi-objective baselines. Further analysis of the Pareto frontier and sensitivity to constraint thresholds demonstrates that CLTR provides a principled and interpretable mechanism for navigating trade-offs in ranking models, with direct implications for large-scale production systems.