ADOPT: A Modified Adam Optimizer with Guaranteed Convergence for Any Beta-2 Value

A new modification to Adam called ADOPT enables optimal convergence rates regardless of the β₂ parameter choice. The key insight is adding a simple term to Adam’s update rule that compensates for potential convergence issues when β₂ is set suboptimally.

Technical details: – ADOPT modifies Adam’s update rule by introducing an additional term proportional to (1-β₂) – Theoretical analysis proves O(1/√T) convergence rate for any β₂ ∈ (0,1) – Works for both convex and non-convex optimization – Maintains Adam’s practical benefits while improving theoretical guarantees – Requires no additional hyperparameter tuning

Key results: – Matches optimal convergence rates of SGD for smooth non-convex optimization – Empirically performs similarly or better than Adam across tested scenarios – Provides more robust convergence behavior with varying β₂ values – Theoretical guarantees hold under standard smoothness assumptions

I think this could be quite useful for practical deep learning applications since β₂ tuning is often overlooked compared to learning rate tuning. Having guaranteed convergence regardless of β₂ choice reduces the hyperparameter search space. The modification is simple enough that it could be easily incorporated into existing Adam implementations.

However, I think we need more extensive empirical validation on large-scale problems to fully understand the practical impact. The theoretical guarantees are encouraging but real-world performance on modern architectures will be the true test.

TLDR: ADOPT modifies Adam with a simple term that guarantees optimal convergence rates for any β₂ value, potentially simplifying optimizer tuning while maintaining performance.

Full summary is here. Paper here.