On the Trade-Off Between Flatness and Optimization in Distributed Learning.

Area of Science:

• Machine Learning
• Optimization Theory
• Distributed Systems

Background:

• Convergence to flat local minima enhances generalization in learning algorithms.
• Understanding algorithm behavior around local minima in non-convex settings is crucial.

Purpose of the Study:

• To propose a theoretical framework for evaluating stochastic gradient algorithms in distributed learning.
• To compare decentralized and centralized learning strategies concerning local minima behavior and classification accuracy.

Main Methods:

• Theoretical analysis of stochastic gradient algorithms in non-convex environments.
• Comparison of decentralized (consensus, diffusion) and centralized learning strategies.
• Evaluation of algorithm performance based on flatness of local minima and optimization error.

Main Results:

• Decentralized strategies escape local minima faster and converge to flatter minima than centralized ones.
• Diffusion strategy in decentralized methods shows better excess-risk performance than consensus.
• Classification accuracy depends on both minimum flatness and the algorithm's ability to approach it.

Conclusions:

• Decentralized strategies offer enhanced classification accuracy by balancing flatness and optimization performance.
• Diffusion strategy outperforms consensus in achieving better generalization.
• The interplay between flatness and optimization error is key to superior performance in non-convex distributed learning.