Auxiliary Function Root Finding for Stable ML Cost Optimization
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Solution Overview
Problem
Conventional methods for finding local minimum points of machine learning cost functions, such as gradient descent and second-order techniques, are inefficient, resource-intensive, and numerically unstable, leading to prolonged processing times and inaccurate results.
Innovation Solution
The use of an auxiliary function based on the gradient of the cost function, combined with a modified Newton's method, to identify roots of the auxiliary function, which are then used to update machine learning model parameters, reducing the number of iterations required and maintaining numerical stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If gradient descent is used to find local minimum points of cost functions, then the method is simple to implement, but it requires a large number of iterations and small step sizes which increases processing resources and time
Solution Approach 1:
The patent introduces an auxiliary function as an intermediary between the gradient descent method and the cost function optimization. This auxiliary function transforms the gradient vector into a scalar value that can be optimized more efficiently, serving as a mediator that simplifies the optimization process while improving convergence speed
Solution Approach 2:
The patent changes the parameter representation by transforming the gradient vector (multiple parameters) into a scalar auxiliary function (single parameter). This parameter transformation allows the use of more efficient optimization methods on the auxiliary function while still achieving cost function minimization
2Productivity
If second-order information methods are used to optimize gradient descent, then convergence speed improves, but computational expense and numerical instability increase
Solution Approach 1:
The patent extracts only the essential information needed for optimization by creating an auxiliary function from the gradient vector. Instead of using full second-order information (Hessian matrix) which is computationally expensive and unstable, the method extracts a scalar representation that captures the necessary optimization direction while avoiding the computational burden and numerical instability of complete second-order methods
Data Source
AI summary
Certain aspects of the present disclosure provide techniques for optimizing a cost function of a deep learning algorithm. One example method generally includes executing, via a processing apparatus, the machine learning model, wherein the machine learning model can be optimized using gradient descent and evaluating output of the machine learning model using a cost function. The method further involves determining a gradient of the cost function and generating an auxiliary function based on the gradient. The method further involves identifying a root of the auxiliary function corresponding to a minimum point of the cost function, wherein calculation of the root is numerically stable and updating the machine learning model based on the root of the auxiliary function.