Differentially Private Stochastic Gradient Descent with Error-Feedback Approach to Eliminate Clipping Bias

Grunnleggende konsepter

The proposed DiceSGD algorithm uses a clipped error-feedback mechanism to eliminate the constant clipping bias in differentially private stochastic gradient descent (DPSGD) while maintaining the same level of privacy guarantee.

Sammendrag

The paper presents the DiceSGD algorithm as an alternative to the commonly used DPSGD with gradient clipping (DPSGD-GC). DPSGD-GC provides a strong theoretical privacy guarantee but suffers from performance degradation due to the constant bias introduced by gradient clipping.
The key insights are:

DiceSGD introduces an error-feedback (EF) mechanism to accumulate the clipping error and feed it back to the next update. This allows DiceSGD to eliminate the constant clipping bias, unlike DPSGD-GC.

The authors provide a novel convergence analysis for DiceSGD under general non-convex and Lipschitz-smooth assumptions. They show that DiceSGD can achieve the same convergence rate as non-private SGD without the constant bias.

The authors also develop an algorithm-specific Rényi-DP analysis for DiceSGD, which accounts for the privatized state and the non-privatized hidden state (the error feedback). They show that DiceSGD satisfies (ε, δ)-DP by injecting a slightly larger DP noise compared to DPSGD-GC.

Empirical results on image classification and natural language processing tasks demonstrate that DiceSGD outperforms DPSGD-GC in terms of model accuracy while maintaining the same level of DP guarantee.

The key contribution of this work is the design of the clipped EF mechanism that allows DiceSGD to eliminate the clipping bias without compromising the DP guarantee, and the novel convergence and privacy analyses to support the algorithm.

Statistikk

The magnitude of the per-sample gradient is bounded by a constant G.
The variance of the stochastic gradient estimation is bounded by a constant σ^2/N.

Sitater

"Recent work Koloskova et al. (2023) has shown a negative result that, under the general assumptions for SGD, regardless of the choice of clipping threshold and stepsize, DPSGD-GC converges with a constant bias term, meaning in the limit the DPSGD-GC algorithm only converges to a neighborhood of the optimal or stationary solution."
"Therefore, how to properly choose the clipping threshold in practice is more of an art than a science."

Viktige innsikter hentet fra

Differentially Private SGD Without Clipping Bias: An Error-Feedback Approach

by Xinwei Zhang... klokken arxiv.org 04-18-2024

https://arxiv.org/pdf/2311.14632.pdf

Dypere Spørsmål

How can the proposed DiceSGD algorithm be extended to the distributed or federated learning setting while maintaining the same level of privacy guarantee and performance improvement over DPSGD-GC?

The DiceSGD algorithm can be extended to the distributed or federated learning setting by incorporating the clipped error-feedback mechanism into the communication process between the central server and the participating clients. In a distributed setting, each client can compute the clipped gradients and the clipping error locally, then send these privatized updates to the central server. The central server can aggregate these updates using the same clipped error-feedback mechanism to eliminate biases introduced by gradient transformations. By ensuring that the clipping thresholds are consistent across all clients and the central server, the algorithm can maintain the same level of privacy guarantee and performance improvement over DPSGD-GC in a distributed or federated learning setting.

Can the clipped error-feedback mechanism be applied to other optimization algorithms beyond SGD to eliminate biases introduced by gradient transformations?

Yes, the clipped error-feedback mechanism can be applied to other optimization algorithms beyond SGD to eliminate biases introduced by gradient transformations. The key idea behind the clipped error-feedback mechanism is to accumulate the error between the clipped update and the unclipped update at each iteration and feed this clipped error back into the optimization process. This mechanism can help in compensating for biases introduced by gradient clipping and can be integrated into various optimization algorithms that involve gradient transformations. Algorithms such as Adam, RMSprop, or Adagrad can benefit from the clipped error-feedback mechanism to mitigate biases caused by gradient clipping and improve convergence properties.

What are the potential applications of the DiceSGD algorithm beyond machine learning, where the elimination of bias in privatized updates could be beneficial?

The DiceSGD algorithm's ability to eliminate bias in privatized updates can have applications beyond machine learning in various fields where differential privacy and bias mitigation are crucial. Some potential applications include:

Healthcare Data Analysis: In healthcare analytics, where sensitive patient data is involved, ensuring privacy and mitigating biases in data analysis are paramount. The DiceSGD algorithm can be applied to train models on healthcare data while maintaining privacy guarantees and reducing biases introduced during the training process.

Financial Data Processing: In the financial sector, where privacy and fairness are essential, DiceSGD can be used to train models on financial data while preserving privacy and minimizing biases in decision-making processes.

Smart Grid Optimization: In energy systems and smart grid optimization, where data privacy and accuracy are critical, DiceSGD can help in training models on sensitive energy consumption data while ensuring differential privacy and reducing biases in the optimization process.

Supply Chain Management: In supply chain management, where data sharing among multiple stakeholders is common, DiceSGD can be employed to train models on shared data while protecting privacy and addressing biases in the decision-making algorithms.

Overall, the DiceSGD algorithm's bias elimination capabilities make it versatile for applications across various domains where differential privacy and bias mitigation are essential considerations.