Optimization Apparatus for Differential Private Stochastic Gradient Descent
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Solution Overview
Problem
The calculation time for differential private stochastic gradient descent (DP-SGD) is prolonged due to the necessity of calculating the norm of the gradient for each data point during gradient clipping.
Innovation Solution
An optimization apparatus that randomly samples data, calculates gradients for an l-Lipschitz continuous loss function, adds noise following a Gaussian distribution, and updates parameters without the need for gradient clipping, allowing parallel calculation of gradients with noise addition.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If gradient clipping is performed by calculating the L2 norm for each data point, then differential privacy is guaranteed, but calculation time increases
Solution Approach 1:
The patent extracts and removes the gradient clipping step from the DP-SGD process. By using a different approach that relies on the Lipschitz continuity property of the loss function rather than explicit gradient clipping, the method eliminates the computational bottleneck of calculating L2 norms for each data point while still maintaining differential privacy guarantees through the inherent properties of the optimized function
Solution Approach 2:
The patent changes the approach from modifying gradient parameters through clipping to modifying the loss function parameters by ensuring Lipschitz continuity. This parameter change allows the system to achieve differential privacy through the mathematical properties of the loss function rather than through post-processing gradient clipping, thereby reducing calculation time
2Reliability
If gradient clipping is applied to restrict L2 norm, then privacy protection is maintained, but device complexity increases
Solution Approach 1:
The patent removes the gradient clipping mechanism from the algorithm. Instead of implementing complex clipping logic that requires calculating and comparing L2 norms against thresholds for each data point, the solution extracts the privacy protection mechanism and implements it through the simpler Lipschitz continuous loss function formulation, thereby reducing algorithmic complexity
Solution Approach 2:
The loss function itself provides the privacy protection mechanism through its Lipschitz continuity property. The function structure inherently limits gradient magnitudes without requiring external clipping operations, making the system self-regulating and reducing the complexity of additional control mechanisms
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach reduces the calculation time of DP-SGD by eliminating the requirement for gradient clipping, enabling faster parameter updates while maintaining differential privacy.
Implementation Method 1
a noise addition unit that adds noise according to a Gaussian distribution to the gradient to calculate a gradient after noise addition
Data Source
AI summary
An optimization apparatus according to one embodiment is an optimization apparatus for optimizing a function having a parameter is provided. The optimization apparatus comprises: a sub-sampling unit that randomly samples a predetermined number of pieces of data from a given data set, to create a data aggregate consisting of the predetermined number of pieces of data; a gradient calculation unit that calculates a gradient related to the parameter of a l-Lipschitz continuous loss function, for each of the pieces of data included in the data aggregate; a noise addition unit that adds noise according to a Gaussian distribution to the gradient to calculate a gradient after noise addition; and a parameter update unit that updates the parameter by using the gradient obtained after the noise addition.