ZO-signSGD Black-Box Optimization via Gradient Blending
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Solution Overview
Problem
Existing black-box optimization methods face challenges in generating adversarial examples without first-order information, particularly in machine learning scenarios where explicit gradient expressions are difficult to obtain, limiting their practical application in generating effective adversarial attacks.
Innovation Solution
The development of a zeroth-order sign-based descent algorithm (ZO-signSGD) that uses an average gradient estimator with forward difference, variance reduction via gradient blending, and binary quantization to optimize black-box systems, allowing for efficient and secure gradient-free optimization with improved convergence rates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional zeroth-order optimization methods are used for black-box optimization, then gradient-free optimization is achieved, but the convergence rate is slow and requires impractical assumptions (b=O(T))
Solution Approach 1:
The gradient estimation process is segmented into multiple independent random direction evaluations. Instead of using a single gradient estimate, the algorithm divides the estimation into b independent directions, each contributing to the final gradient estimate. This segmentation allows for better statistical properties and faster convergence without requiring impractical assumptions about batch size relationships with iteration count.
Solution Approach 2:
The algorithm changes the parameter representation by using binary quantization of gradient estimates. Instead of working with continuous gradient values, the method quantizes gradients to binary values, which reduces communication overhead and computational complexity while maintaining effective convergence rates in black-box settings.
2Productivity
If full gradient information is used in white-box settings, then optimization performance is improved, but information leakage occurs in black-box settings
Solution Approach 1:
The algorithm extracts only the necessary sign information from gradient estimates rather than using full gradient values. By taking out only the binary sign component and discarding the magnitude information, the method achieves effective optimization in black-box settings while preventing information leakage about the internal structure of the target system.
Solution Approach 2:
The algorithm uses disposable random direction vectors that are generated independently for each gradient estimation. These random directions are cheap to generate and discard, allowing the system to obtain unbiased gradient estimates without requiring persistent or reusable components that could leak information about the system being optimized.
3Stability of the object's composition
If variance reduction techniques are applied to gradient estimation, then convergence stability is improved, but computational overhead increases
Solution Approach 1:
The algorithm performs preliminary gradient estimation in multiple random directions before finalizing the gradient update. By pre-computing gradients in b different directions and then combining them, the method reduces variance in the final gradient estimate without requiring excessive computational resources during the main optimization loop.
Solution Approach 2:
The variance reduction is achieved through the inherent structure of the algorithm itself rather than requiring external variance reduction techniques. The multiple random direction evaluations naturally provide variance reduction through averaging, making the system self-sufficient in managing its own gradient estimation quality without additional computational overhead from external variance reduction mechanisms.
Data Source
AI summary
A black box optimization method, system, and computer program product include implementing an average gradient estimator using a forward difference of function values at multiple random directions, performing variance reduction via gradient blending with an output of the average gradient estimator using a control variate, and performing binary quantization of a result of the variance reduction.