MoRe method accelerates multi-objective learning with 2x faster convergence
New algorithm improves stochastic gradient descent for conflicting objectives, cutting error rate by half.
Multi-objective learning (MOL) is critical for tasks like training large language models with multiple loss terms (e.g., accuracy, fairness, energy). The standard multi-gradient descent algorithm (MGDA) iteratively computes a common descent direction that avoids conflicts between objectives. In stochastic settings, however, the vanilla stochastic MGDA (SMG) suffers from noise-induced bias in the update direction, leading to slow convergence. Huang and Chen (arXiv:2607.15412) prove that the conflict-avoidant (CA) direction is only 1/2-Hölder continuous with respect to the Jacobian matrix—and this exponent cannot be improved in the worst case, explaining SMG's suboptimal rate.
Leveraging this insight, the authors propose MoRe (multi-objective regularity-aware), which detects when the subproblem is “regular” (i.e., gradients are Lipschitz continuous) and uses the CA update; otherwise it falls back to fixed scalarization. This adaptive mechanism yields a theoretical convergence rate of O(T^{-1/2}) in nonconvex settings—compared to SMG's O(T^{-1/4})—while maintaining per-iterate conflict avoidance. Experiments confirm MoRe outperforms prior methods on multi-task benchmarks, offering a practical tool for AI practitioners juggling competing objectives in training pipelines.
- MoRe improves convergence from O(T^{-1/4}) to O(T^{-1/2}) for nonconvex multi-objective optimization.
- The conflict-avoidant direction is proven to be 1/2-Hölder continuous; Lipschitz continuity only holds under additional regularity.
- Empirical results show MoRe achieves better multi-task performance while guaranteeing per-iterate conflict avoidance.
Why It Matters
Faster, more stable multi-objective training means better models for tasks like fairness, robustness, and multi-modal learning.