On Optimization Complexity of Second-Order Certified Unlearning

Source

Source name: arXiv
Source kind: paper
Authors / organization: Nikita Doikov, Anastasia Koloskova
Venue: arXiv: cs.LG
Published: 2026-07-22
Collected: 2026-07-23
URL: http://arxiv.org/abs/2607.20192v1
PDF: https://arxiv.org/pdf/2607.20192v1
DOI: UNKNOWN

Plain-Language Brief

The authors investigate the complexity of removing trained data from machine learning models, focusing on certified unlearning and optimization accuracy. They propose new bounds on the distance between initial and unlearned models using uniformly convex regularizers. The authors also develop a second-order unlearning algorithm that achieves fast rates for linear models with quasi-self-concordant losses.

What the Document Says

The text discusses machine unlearning, the removal of trained data from a model.
The focus is on certified unlearning and optimization accuracy.
They use uniformly convex regularizers to formalize the goal of an unlearning algorithm.
New bounds on the distance between initial and unlearned models are proven using a substitute for generalization error.
A novel second-order unlearning algorithm is developed with an anisotropic Gaussian mechanism and global convergence.
Fast rates are proved for the method in achieving certified unlearning for linear models with quasi-self-concordant losses.

Key Concepts Mentioned

Machine Unlearning
Certified Unlearning
Optimization Accuracy
Uniformly Convex Regularizers
Generalization Error
Anisotropic Gaussian Mechanism
Global Convergence
Quasi-self-concordant Losses

Claims Made by the Document

The removal of well-predicted data leads to a simpler optimization problem.
Second-order unlearning provides a provable benefit over first-order methods.

Evidence Used

The text states that if the removed data is well-predicted by the unlearned model, the corresponding optimization problem is simple.
The authors prove fast rates for their second-order method in achieving certified unlearning for linear models.

Methods / Approach

Using uniformly convex regularizers
Developing a second-order unlearning algorithm with an anisotropic Gaussian mechanism

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

We study machine unlearning: the removal of memorized training data from a trained model. Specifically, we investigate the algorithmic complexity of certified unlearning from an optimization perspective. We formalize the goal of an unlearning algorithm as simultaneously achieving certified unlearning and optimization accuracy. Utilizing the notion of uniformly convex regularizers, we prove new bounds on the distance between initial and unlearned models using a novel substitute for generalization error. Thus we theoretically demonstrate that if the removed data is well-predicted by the unlearned model, the corresponding optimization problem is simple. Furthermore, we develop a new second-order unlearning algorithm with an anisotropic Gaussian mechanism and state-of-the-art global convergence. We prove fast rates for our method in achieving certified unlearning for linear models with quasi-self-concordant losses. As a direct application, our theory covers unlearning for logistic and exponential regressions and shows a provable benefit of utilizing second-order information compared to first-order unlearning methods.