Adaptive Learning Rate Optimization for Neural Network Convergence
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Solution Overview
Problem
Existing adaptive optimization techniques for machine-learned models, such as RMSprop and Adam, often fail to converge in settings with nonconvex loss functions and dense gradients due to rapid decay of the learning rate and limited reliance on past gradients.
Innovation Solution
The proposed method involves determining a gradient of a loss function and a candidate learning rate control value based on this gradient. It compares this candidate value to a maximum previously observed learning rate control value, ensuring that the current learning rate does not increase over iterations by selecting the maximum of the two values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exponential moving averages of squared past gradients are used to mitigate rapid decay of learning rate, then convergence in nonconvex settings is improved, but convergence fails in settings with large but rare gradients due to limited reliance on past gradients
Solution Approach 1:
The patent applies preliminary action by maintaining a running maximum of learning rate control values observed throughout training. Before each parameter update, the algorithm compares the current candidate learning rate control value against the historical maximum and uses the larger of the two, ensuring that once a large gradient is encountered, its impact persists indefinitely rather than decaying. This preliminary tracking of maximum values prevents the learning rate from being overly constrained by rare large gradients while still adapting to the overall training trajectory.
2Adaptability or versatility
If sum of squares of all past gradients is used in Adagrad, then performance is improved for sparse settings, but performance deteriorates in nonconvex settings with dense gradients due to rapid decay of learning rate
Solution Approach 1:
The patent applies dynamics by making the learning rate control value adaptive based on the training history. Instead of using a fixed decay schedule or simple sum of squares, the algorithm dynamically adjusts the learning rate control by comparing current gradients against historical maximums. The learning rate control value increases when large gradients are encountered and maintains this increased level, allowing the algorithm to adapt to both sparse and dense gradient settings without the rapid decay problem that plagues Adagrad in nonconvex optimization.
3Stability of the object's composition
If exponential averaging limits reliance to past few gradients, then learning rate decay is mitigated, but influence of large but rare gradients dies out quickly leading to poor convergence
Solution Approach 1:
The patent applies continuity of useful action by ensuring that the maximum learning rate control value observed during training persists indefinitely. Rather than allowing the learning rate control to decay or be overwritten by subsequent smaller gradients, the algorithm maintains the historical maximum once established. This continuous retention of the maximum learning rate control value ensures that large but rare gradients continue to influence the optimization process throughout training, providing stable and reliable convergence behavior.
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 learning rate while also ensuring that the learning rate is non-increasing.