Summary of Mgda Converges Under Generalized Smoothness, Provably, by Qi Zhang et al.
MGDA Converges under Generalized Smoothness, Provably
by Qi Zhang, Peiyao Xiao, Shaofeng Zou, Kaiyi Ji
First submitted to arxiv on: 29 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper presents a novel approach to multi-objective optimization (MOO) for neural networks like LSTMs and Transformers. Traditional algorithms rely on assumptions that don’t hold in these domains. The authors introduce a more realistic class of generalized -smooth loss functions, which they analyze using the multiple gradient descent algorithm (MGDA) and its stochastic version. They provide convergence guarantees for solving MOO problems, achieving an -accurate Pareto stationary point with guaranteed average conflict-avoidant distance. The algorithms require (^{-2}) samples in deterministic settings and (^{-4}) samples in stochastic settings. An efficient variant, MGDA-FA, is also introduced, which achieves the same performance guarantees with only (1) time and space. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper solves a big problem in artificial intelligence. Neural networks like LSTMs and Transformers are used to do many things at once, but it’s hard to make them work well together. The authors find a new way to make these networks cooperate by introducing a special type of math problem called multi-objective optimization (MOO). They test their idea using a clever algorithm and show that it can solve MOO problems in a more efficient way than before. |
Keywords
» Artificial intelligence » Gradient descent » Optimization
