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

2026-06-01

AI Summary

Existing machine unlearning methods struggle to simultaneously achieve effective forgetting and preservation of model utility, lacking a quantifiable mechanism to balance these competing objectives. This work proposes Hardness-Aware Multi-objective Unlearning (HAMU), which introduces, for the first time, a “hardness” metric based on the similarity between forget and retain data to characterize the degree of objective conflict. HAMU formulates a theoretically grounded constrained optimization framework that enables controllable and terminable unlearning. By integrating non-convex weight updates with parallelization strategies, HAMU significantly outperforms current approaches on large-scale vision and language models, achieving strong forgetting guarantees while minimizing performance degradation on retained tasks.

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.

Problem

• machine unlearning
• forget quality
• retain utility
• hardness-aware
• constrained optimization

Innovation

• machine unlearning
• hardness-aware optimization
• constrained optimization
• forget quality
• retain utility