Adaptive Learning Rate Control for Stable Non-Convex Convergence
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Solution Overview
Problem
Existing adaptive optimization techniques for machine-learned models, such as Adagrad, RMSprop, and Adam, struggle with rapid decay of the effective learning rate in non-convex settings and sparse gradient scenarios, leading to poor convergence and inefficiencies.
Innovation Solution
The proposed method, referred to as Yogi, employs additive updates to a learning rate control value that allows the effective learning rate to increase or decrease relative to previous iterations, controlled by the gradient of the loss function and the most recent learning rate control value, preventing overly-significant changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Adagrad uses a sum of squares of all past gradients to force strictly decreasing effective learning rate, then convergence is improved in sparse settings, but performance deteriorates in non-convex settings due to rapid decay
Solution Approach 1:
The patent applies dynamics by allowing the effective learning rate to dynamically increase or decrease based on current gradient magnitude relative to historical averages, rather than forcing monotonic decay. The effective learning rate is computed as ηt = η / (1 + γ * (gt² / mt)), where mt is the moving average of squared gradients. This dynamic adjustment enables the learning rate to adapt to changing optimization landscapes, resolving the contradiction between convergence reliability and performance in non-convex settings.
2Productivity
If Adam uses exponential moving averages of squared past gradients to limit reliance on recent gradients, then performance in non-convex settings is improved, but convergence deteriorates in sparse settings where small gradients dominate
Solution Approach 1:
The patent applies parameter changes by introducing a decay factor γ that controls the balance between historical gradient information and current gradient magnitude. The effective learning rate formula ηt = η / (1 + γ * (gt² / mt)) allows adjustment of how much weight is given to past gradients versus current gradients. By tuning γ, the system can prevent small gradients from dominating the moving average while still benefiting from historical information, thus improving convergence in sparse settings while maintaining non-convex performance.
3Speed
If the effective learning rate is allowed to increase freely, then convergence speed is improved, but stability deteriorates due to oscillations
Solution Approach 1:
The patent applies feedback by continuously monitoring the ratio of current gradient squared to moving average of squared gradients (gt² / mt). This feedback mechanism automatically adjusts the effective learning rate in proportion to the current optimization state. When gradients are large, the learning rate decreases; when gradients are small, the learning rate increases. This proportional feedback ensures both fast convergence and stability, preventing oscillations while maintaining adaptive speed adjustment.
Data Source
AI summary
Generally, the present disclosure is directed to systems and methods that perform adaptive optimization with improved convergence properties. The adaptive optimization techniques described herein are useful in various optimization scenarios, including, for example, training a machine-learned model such as, for example, a neural network. In particular, according to one aspect of the present disclosure, a system implementing the adaptive optimization technique can, over a plurality of iterations, employ an adaptive effective learning rate while also ensuring that the effective learning rate is non-increasing.