# MUNBa: Machine Unlearning via Nash Bargaining

arXiv: https://arxiv.org/abs/2411.15537 · HTML: https://mlsanity.com/paper/2411.15537/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 61 of its 87 references that are in the map.
- First posted on arXiv 23 Nov 2024.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 61)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models](https://mlsanity.com/paper/2211.05105/) (2022)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Unified Concept Editing in Diffusion Models](https://mlsanity.com/paper/2308.14761/) (2023)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.17591/) (2023)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [In-Context Unlearning: Language Models as Few Shot Unlearners](https://mlsanity.com/paper/2310.07579/) (2023)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [To Generate or Not? Safety-Driven Unlearned Diffusion Models Are Still Easy To Generate Unsafe Images ... For Now](https://mlsanity.com/paper/2310.11868/) (2023)
- [fastai: A Layered API for Deep Learning](https://mlsanity.com/paper/2002.04688/) (2020)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [Selective Amnesia: A Continual Learning Approach to Forgetting in Deep Generative Models](https://mlsanity.com/paper/2305.10120/) (2023)

## Built on by (most cited first, 17 of 17)

- [Set You Straight: Auto-Steering Denoising Trajectories to Sidestep Unwanted Concepts](https://mlsanity.com/paper/2504.12782/) (2025)
- [Machine Unlearning under Retain-Forget Entanglement](https://mlsanity.com/paper/2603.26569/) (2026)
- [Erasing Concepts, Steering Generations: A Comprehensive Survey of Concept Suppression](https://mlsanity.com/paper/2505.19398/) (2025)
- [A Comprehensive Survey on Concept Erasure in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2502.14896/) (2025)
- [Rethinking Machine Unlearning in Image Generation Models](https://mlsanity.com/paper/2506.02761/) (2025)
- [Generative Model Unlearning: A Survey through Target Events, Unlearning Operators, and Evaluation Protocols](https://mlsanity.com/paper/2507.19894/) (2025)
- [Tackling Fake Forgetting through Uncertainty Quantification](https://mlsanity.com/paper/2501.19403/) (2025)
- [ACE: Attentional Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2504.11850/) (2025)
- [One-Point Contraction: Erasing Representational Separability toward Irreversible Deep Forgetting](https://mlsanity.com/paper/2507.07754/) (2025)
- [Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraints](https://mlsanity.com/paper/2605.30825/) (2026)
- [IMU: Influence-guided Machine Unlearning](https://mlsanity.com/paper/2508.01620/) (2025)
- [Designing to Forget: Deep Semi-parametric Models for Unlearning](https://mlsanity.com/paper/2603.22870/) (2026)
- [Harmonized Tabular-Image Fusion via Gradient-Aligned Alternating Learning](https://mlsanity.com/paper/2604.01579/) (2026)
- [From Competition to Collaboration: Designing Sustainable Mechanisms Between LLMs and Online Forums](https://mlsanity.com/paper/2602.04572/) (2026)
- [Multi-Objective Reference-Aligned Machine Unlearning](https://mlsanity.com/paper/2606.00399/) (2026)
- [On the Plasticity Collapse in Continual Machine Unlearning](https://mlsanity.com/paper/2608.29513/) (2026)
- [Forget or Fine-tune? A Comparative Study of Machine Unlearning Strategies for Noisy Label Correction](https://mlsanity.com/paper/2608.30046/) (2026)

## Abstract (arXiv)

Machine Unlearning (MU) aims to selectively erase harmful behaviors from models while retaining the overall utility of the model. As a multi-task learning problem, MU involves balancing objectives related to forgetting specific concepts/data and preserving general performance. A naive integration of these forgetting and preserving objectives can lead to gradient conflicts and dominance, impeding MU algorithms from reaching optimal solutions. To address the gradient conflict and dominance issue, we reformulate MU as a two-player cooperative game, where the two players, namely, the forgetting player and the preservation player, contribute via their gradient proposals to maximize their overall gain and balance their contributions. To this end, inspired by the Nash bargaining theory, we derive a closed-form solution to guide the model toward the Pareto stationary point. Our formulation of MU guarantees an equilibrium solution, where any deviation from the final state would lead to a reduction in the overall objectives for both players, ensuring optimality in each objective. We evaluate our algorithm's effectiveness on a diverse set of tasks across image classification and image generation. Extensive experiments with ResNet, vision-language model CLIP, and text-to-image diffusion models demonstrate that our method outperforms state-of-the-art MU algorithms, achieving a better trade-off between forgetting and preserving. Our results also highlight improvements in forgetting precision, preservation of generalization, and robustness against adversarial attacks.