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This research establishes rigorous theoretical bounds for machine unlearning, demonstrating that simple perturbation methods suffice for in-distribution data but fail for out-of-distribution cases where complexity exceeds retraining. To address this gap, the authors propose a robust noisy gradient descent variant that provably amortizes time complexity while maintaining utility. These findings provide a critical foundation for deploying privacy-preserving unlearning with formal guarantees rather than relying on heuristic approaches.
The Utility and Complexity of in- and out-of-Distribution Machine Unlearning
arXiv:2412.09119v3 Announce Type: replace Abstract: Machine unlearning, the process of selectively removing data from trained models, is increasingly crucial for addressing privacy concerns and knowledge gaps post-deployment. Despite this importance, existing approaches are often heuristic and lack formal guarantees. In this paper, we analyze the fundamental utility, time, and space complexity trade-offs of approximate unlearning, providing rigorous certification analogous to differential privacy. For in-distribution forget data -- data similar to the retain set -- we show that a surprisingly simple and general procedure, empirical risk minimization with output perturbation, achieves tight unlearning-utility-complexity trade-offs, addressing a previous theoretical gap on the separation from unlearning "for free" via differential privacy, which inherently facilitates the removal of such data. However, such techniques fail with out-of-distribution forget data -- data significantly different from the retain set -- where unlearning time complexity can exceed that of retraining, even for a single sample. To address this, we propose a new robust and noisy gradient descent variant that provably amortizes unlearning time complexity without compromising utility.
Abstract:Machine unlearning, the process of selectively removing data from trained models, is increasingly crucial for addressing privacy concerns and knowledge gaps post-deployment. Despite this importance, existing approaches are often heuristic and lack formal guarantees. In this paper, we analyze the fundamental utility, time, and space complexity trade-offs of approximate unlearning, providing rigorous certification analogous to differential privacy. For in-distribution forget data -- data similar to the retain set -- we show that a surprisingly simple and general procedure, empirical risk minimization with output perturbation, achieves tight unlearning-utility-complexity trade-offs, addressing a previous theoretical gap on the separation from unlearning "for free" via differential privacy, which inherently facilitates the removal of such data. However, such techniques fail with out-of-distribution forget data -- data significantly different from the retain set -- where unlearning time complexity can exceed that of retraining, even for a single sample. To address this, we propose a new robust and noisy gradient descent variant that provably amortizes unlearning time complexity without compromising utility.
Machine Learning (cs.LG); Cryptography and Security (cs.CR); Optimization and Control (math.OC)
arXiv:2412.09119 [cs.LG]
(or arXiv:2412.09119v3 [cs.LG] for this version)
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