Editing Is a Bargaining Game: Balanced Knowledge Editing in Large Language Models

Large Language Models (LLMs) are prone to generating incorrect or outdated information, thereby necessitating efficient and precise mechanisms for knowledge updates. Existing knowledge editing approaches, however, often encounter conflicts between two competing objectives: maintaining existing knowledge (preservation) and incorporating new information (editing). During gradient-based optimization, these conflicting objectives can lead to imbalanced update directions, where one gradient dominates, ultimately resulting in suboptimal learning dynamics. To address this challenge, we propose a balanced knowledge editing framework inspired by Nash bargaining theory. Our method guides the optimization process toward a Pareto stationary point, ensuring an equilibrium solution wherein any deviation from the final state would degrade the overall performance with respect to both objectives. This guarantees optimality in preserving prior knowledge while integrating new information. We empirically validate the effectiveness of our approach across a range of evaluation metrics on standard benchmark datasets. Extensive experiments show that our method consistently outperforms state-of-the-art techniques, achieving a superior balance between knowledge preservation and update accuracy.