Yogi Learning Rate Control for Sparse Gradient Convergence
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Solution Overview
Problem
Existing adaptive optimization techniques for machine-learned models, such as Adagrad, Adam, and RMSprop, 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, known as Yogi, employs additive updates to the learning rate control value, allowing the effective learning rate to increase or decrease relative to previous iterations in a controlled manner, using the gradient of the loss function and a scaling coefficient, thereby preventing overly-significant changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If exponential moving averages of squared past gradients are used to control learning rate (as in Adam, RMSprop), then rapid decay of effective learning rate is mitigated, but convergence fails in sparse settings where small gradients undesirably dominate the moving average
Solution Approach 1:
The patent applies local quality by treating different gradient scenarios differently through the sign function. When the gradient squared is less than the previous control value, the learning rate is increased (local adaptation for sparse settings). When the gradient squared is greater, the learning rate is decreased (local adaptation for dense settings). This localized response to gradient magnitude resolves the contradiction between stability and convergence reliability.
Solution Approach 2:
The patent implements dynamics by making the learning rate control value adaptive and dynamic rather than static. The control value evolves iteratively based on the relationship between current gradient squared and previous control value, allowing the system to automatically adjust its behavior to match the current optimization landscape, thus achieving both stability and convergence reliability.
2Adaptability or versatility
If sum of squares of all past gradients is used (as in Adagrad), then effective learning rate automatically adjusts on per-feature basis, but effective learning rate decays rapidly in non-convex settings with dense gradients causing gradient descent to get stuck
Solution Approach 1:
The patent inverts the traditional approach by not directly accumulating gradient squares as in Adagrad. Instead, it uses the relationship between current gradient squared and previous control value to determine whether to increase or decrease the control value. This inversion prevents the rapid decay problem while maintaining per-feature adaptation, resolving the contradiction between adaptability and convergence speed.
Solution Approach 2:
The patent makes the learning rate control dynamic by allowing it to increase when gradients are small (sparse settings) and decrease when gradients are large (dense settings). This dynamic behavior contrasts with Adagrad's monotonic decay and resolves the contradiction by adapting the learning rate to the current optimization context, thereby maintaining both adaptability and productivity.
3Device complexity
If vanilla stochastic gradient descent is used, then implementation is simple, but convergence is slow and inefficient compared to adaptive methods
Solution Approach 1:
The patent changes the key parameter of learning rate from a fixed or简单地 decayed value to an adaptively controlled value that responds to gradient characteristics. This parameter change enables the algorithm to achieve fast convergence like adaptive methods while maintaining the simplicity of vanilla SGD, resolving the contradiction between complexity and productivity.
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.