On Nonconvex SGD Under Unbounded Noise With Weak Gradient Lipschitz and Delayed Stochastic Gradient

Area of Science:

• Machine Learning
• Optimization Algorithms
• Nonconvex Optimization

Background:

• Stochastic methods rely on bounded variance, gradient Lipschitz, and unbiased gradients for convergence and generalization.
• These assumptions are often violated in real-world applications, limiting algorithm applicability.

Purpose of the Study:

• To investigate if gradient normalization with momentum can relax common assumptions for stochastic algorithms.
• To demonstrate the effectiveness of this technique in nonconvex scenarios with violated assumptions.

Main Methods:

• Incorporating simple gradient normalization with momentum into Stochastic Gradient Descent (SGD).
• Analyzing convergence and generalization properties under relaxed conditions (unbounded noise, weak Lipschitz, biased gradients).

Main Results:

• SGD with gradient normalization and momentum guarantees convergence and generalization despite unbounded noise.
• The method effectively handles weak gradient Lipschitz conditions and biased stochastic gradients due to delays.
• Demonstrated robustness in nonconvex settings with violated standard assumptions.

Conclusions:

• Gradient normalization with momentum significantly expands the applicability of stochastic algorithms.
• This approach offers greater flexibility for real-world machine learning problems by relaxing restrictive assumptions.