A Robust Certified Machine Unlearning Method Under Distribution Shift
Jinduo Guo, Yinzhi Cao
TL;DR
This paper introduces a distribution-aware certified machine unlearning method using iterative Newton updates with trust region constraints, effectively handling non-i.i.d. deletion requests and distribution shifts.
Contribution
It proposes a novel unlearning framework that improves efficiency and accuracy under non-i.i.d. deletions by incorporating distribution awareness and trust region constraints.
Findings
Enhanced unlearning accuracy under distribution shift
Tighter bounds on gradient residuals
Effective in practical non-i.i.d. deletion scenarios
Abstract
The Newton method has been widely adopted to achieve certified unlearning. A critical assumption in existing approaches is that the data requested for unlearning are selected i.i.d.(independent and identically distributed). However,the problem of certified unlearning under non-i.i.d. deletions remains largely unexplored. In practice, unlearning requests are inherently biased, leading to non-i.i.d. deletions and causing distribution shifts between the original and retained datasets. In this paper, we show that certified unlearning with the Newton method becomes inefficient and ineffective under non-i.i.d. unlearning sets. We then propose a better certified unlearning approach by performing a distribution-aware certified unlearning framework based on iterative Newton updates constrained by a trust region. Our method provides a closer approximation to the retrained model and yields a…
Peer Reviews
Decision·Submitted to ICLR 2026
1. The trust-region wrapper around an approximate Newton step is technically coherent: it preserves a Newton-like search direction while controlling step size by a model-agreement rule under a locally defined ball. 2. The certificate is tied to quantities the algorithm actually estimates in the loop, namely a local gradient Lipschitz constant in the current ball and a spectral-norm bound from power iteration, which makes the residual bound operational rather than symbolic.
1. The clipping rule sets r_t=∥g_t∥/L_t, while L_titself is defined as the local gradient-Lipschitz constant on the ball B(w_t,r_t). Without an a priori radius or an update scheme that defines L_tbefore r_t, the pair (r_t,L_t)is not well defined and the step size cannot be computed from the specification as written. 2. The paper asserts that, under distribution shift, the trust-region scheme “achieves a closer approximation to the retrained model than a one-step Newton update,” yet the formal r
1. The paper establishes a clear mathematical link between biased deletion and distribution shift and shows why this invalidates conventional Newton-based unlearning. Theoretical derivations, including the local smoothness assumption, descent lemma, and convergence bounds, are carefully constructed and logically consistent, giving the work strong analytical credibility. 2. The experimental design closely mirrors the theoretical claims. The authors quantitatively relate posterior KL divergence
1. The experiments are based on small datasets such as MNIST and CIFAR-10, and the models used are relatively simple. It is uncertain whether the proposed method would still show a clear advantage when tested on larger and more complex networks. As model size grows, the extra computation and time required by the trust-region updates may reduce or even cancel out the observed gains. 2. It would be nice if the paper can include more baselines in the comparisons. 3. The paper briefly mentions po
The machine unlearning problem is timely. Being able to handle non iid data removal is important. The paper is generally clearly written. By using iterative updates, the method only rely on local Lipschitz constants. The use of trust region method make it possible to accommodate non-iid data removal and distribution shift.
The novelty is somewhat limited, this paper combines a few existing ideas. More importantly, unlearning is usually from the context of multi-agent setup. The usage of TR would make it very difficult to generalize to the scenarios of federated learning setting, since coordinated global search required by TR is either very expensive or not possible to implement in distributed setting. The authors need to really motivate well the usage of centralized unlearning methods in any practical settings. T
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Taxonomy
TopicsMachine Learning and Data Classification · Machine Learning and Algorithms · Stochastic Gradient Optimization Techniques