Regularity-Aware Stochastic MGDA with Adaptive Conflict-Avoidant Update Direction Control

2026-07-16 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A new method, Regularity-Aware Stochastic MGDA (MoRe), addresses the suboptimal convergence of vanilla stochastic Multi-Gradient Descent Algorithm (SMG) in multi-objective learning. SMG suffers from a slow Õ(£T¯¹/´) convergence rate in nonconvex settings due to noise from mini-batch sampling biasing its conflict-avoidant (CA) update direction. The research reveals that the CA direction is 1/2-Holder continuous, but can achieve Lipschitz continuity under specific regularity conditions. MoRe leverages this insight by employing CA direction updates when the subproblem is regular and switching to fixed scalarization otherwise. This adaptive approach theoretically improves the convergence rate from Õ(£T¯¹/´) to Õ(£T¯¹/²) and provides per-iterate conflict-avoidance guarantees. Empirical results validate MoRe's effectiveness and its consistent convergence behavior.

Key takeaway

For AI Scientists developing multi-objective learning systems, consider integrating the Regularity-Aware Stochastic MGDA (MoRe) method. Your current stochastic MGDA implementations likely face suboptimal Õ(£T¯¹/´) convergence rates due to gradient noise. Adopting MoRe's adaptive strategy, which switches between conflict-avoidant and scalarization updates based on subproblem regularity, can significantly accelerate convergence to Õ(£T¯¹/²). This improvement is crucial for achieving faster, more stable optimization in complex multi-task scenarios.

Key insights

The MoRe method improves stochastic multi-objective optimization convergence by adaptively exploiting regularity for CA direction updates.

Principles

• CA direction continuity impacts stochastic MGDA convergence.
• Regularity conditions can improve CA direction continuity.
• Adaptive strategies enhance multi-objective optimization.

Method

The MoRe algorithm adaptively uses conflict-avoidant direction updates when the subproblem is regular (exploiting Lipschitz continuity) and switches to fixed scalarization weights otherwise, improving convergence in multi-objective learning.

In practice

• Implement adaptive update strategies in MOL.
• Evaluate subproblem regularity for optimization choices.
• Apply MoRe for faster multi-task learning convergence.

Topics

• Multi-objective Learning
• Stochastic Gradient Descent
• Optimization Algorithms
• Convergence Rates
• Multi-Gradient Descent Algorithm
• Regularity-Aware Optimization

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.