Unified Framework for Gradient Aggregation in Multi-Objective Optimization
A recent paper on arXiv (2605.30452) presents a comprehensive framework for aggregating gradients in multi-objective optimization (MOO). This research establishes optimal rates of convergence to Pareto stationarity, a key performance indicator. At the heart of the analysis is a condition for sufficient alignment, culminating in a theorem that proves convergence is assured when non-conflicting directions are within the convex hull of gradients. Additionally, the framework reveals that feasibility can be attained through projection onto the dual cone, expanding the range of methods that offer convergence assurances.
Key facts
- arXiv paper 2605.30452
- Unifying framework for gradient aggregation in MOO
- Establishes optimal convergence rates to Pareto stationarity
- Sufficient alignment condition is central
- Non-conflicting directions in convex hull of gradients ensure convergence
- Feasibility via projection onto dual cone
- Broadens scope of methods with convergence guarantees
Entities
Institutions
- arXiv