Toward Understanding the Generalizability of Delayed Stochastic Gradient Descent

Area of Science:

• Machine Learning
• Optimization Algorithms

Background:

• Asynchronous stochastic gradient descent (SGD) is vital for large-scale model training.
• Generalization performance of asynchronous delayed SGD is underexplored, with existing bounds being pessimistic.

Purpose of the Study:

• To derive sharper generalization error bounds for SGD with asynchronous delay.
• To investigate the correlation between asynchronous delays and generalization performance.

Main Methods:

• Utilizing generating function analysis to establish the average stability of delayed gradient algorithms.
• Deriving upper bounds on generalization error based on algorithmic stability.

Main Results:

• Established generalization error bounds of $\widetilde{\mathcal {O}}(\frac{T-\tau }{n\tau })$ for quadratic convex and $\widetilde{\mathcal {O}}(\frac{1}{n})$ for strongly convex problems.
• Demonstrated that asynchronous delays can reduce the generalization error of delayed SGD.

Conclusions:

• Asynchronous delays positively impact the generalization of delayed SGD.
• Theoretical findings are validated by experimental results and extend to random delay settings.