New MGDA Method Boosts Multi-Objective Learning Convergence

Multi-objective learning, which involves optimizing several objectives concurrently, often faces challenges with convergence speed in stochastic environments due to gradient noise. Traditional stochastic multi-gradient descent algorithms (SMG) exhibit suboptimal rates because the conflict-avoidant (CA) direction, crucial for updates, is only 1/2-Holder continuous. This inherent continuity limitation contributes to biased updates. A new method, MoRe (Multi-objective Regularity-aware), addresses this by leveraging improved Lipschitz continuity of the CA direction under specific regularity conditions. MoRe intelligently adapts its update strategy: it uses CA direction updates when gradient conflict is high and switches to linear scalarization when the subproblem is regular. This adaptive approach significantly enhances convergence rates in non-convex scenarios, moving from O(T^-1/4) to O(T^-1/2), and maintains conflict-avoidance guarantees.