How Hard Can It Be? Hardness-Aware Multi-Objective Unlearning

Jiangwei Chen, Xinyuan Niu, Rachael Hwee Ling Sim, Zhengyuan Liu, Nancy F. Chen, Bryan Kian Hsiang Low
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:16243-16271, 2026.

Abstract

Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU’s superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26de, title = {How Hard Can It Be? {H}ardness-Aware Multi-Objective Unlearning}, author = {Chen, Jiangwei and Niu, Xinyuan and Sim, Rachael Hwee Ling and Liu, Zhengyuan and Chen, Nancy F. and Low, Bryan Kian Hsiang}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {16243--16271}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26de/chen26de.pdf}, url = {https://proceedings.mlr.press/v306/chen26de.html}, abstract = {Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU’s superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.} }
Endnote
%0 Conference Paper %T How Hard Can It Be? Hardness-Aware Multi-Objective Unlearning %A Jiangwei Chen %A Xinyuan Niu %A Rachael Hwee Ling Sim %A Zhengyuan Liu %A Nancy F. Chen %A Bryan Kian Hsiang Low %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26de %I PMLR %P 16243--16271 %U https://proceedings.mlr.press/v306/chen26de.html %V 306 %X Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU’s superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.
APA
Chen, J., Niu, X., Sim, R.H.L., Liu, Z., Chen, N.F. & Low, B.K.H.. (2026). How Hard Can It Be? Hardness-Aware Multi-Objective Unlearning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:16243-16271 Available from https://proceedings.mlr.press/v306/chen26de.html.

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