Not All Objectives Are Born Equal: Priority-Constrained Descent for Hierarchical Multi-Objective Optimization
The paper proposes an optimizer that treats primary and secondary objectives as a hierarchy, not a symmetric trade-off.
Priority-Constrained Descent keeps the main objective’s descent direction intact while allowing controlled distortion to make progress on secondary goals. A single parameter, `tau`, sets how much that distortion is allowed to matter. The authors report scale invariance, closed-form solutions for two- and three-objective cases, and tests on compression, sparsity, low-rankness, and synthetic settings. They claim PCD outperforms existing methods on Pareto dominance and per-objective performance while guaranteeing secondary progress. HF Daily Papers' note
Priority-Constrained Descent keeps the main objective’s descent direction intact while allowing controlled distortion to make progress on secondary goals. A single parameter, `tau`, sets how much that distortion is allowed to matter. The authors report scale invariance, closed-form solutions for two- and three-objective cases, and tests on compression, sparsity, low-rankness, and synthetic settings. They claim PCD outperforms existing methods on Pareto dominance and per-objective performance while guaranteeing secondary progress. HF Daily Papers' note
score 4