Machine unlearning (MU) aims to efficiently remove sensitive or harmful memory from a pre-trained model. The key challenge is to balance the potential tradeoff between unlearning efficacy and utility preservation, which involves forgetting undesirable information as defined while maintaining the model's original performance. One potential way to tackle this problem is to use multi-objective optimization to jointly optimize both the unlearning and utility preservation objectives. However, existing multi-objective methods only guarantee finding a Pareto-optimal solution without fine-grained control, which causes under-optimization of the unlearning objective. To this end, we first model MU as a constrained optimization problem, that is, optimizing the unlearning objective under the constraint of a bounded increase for utility loss. We then show that solving this optimization problem is equivalent to unilateral gradient surgery on the unlearning objective. To resolve the additional computational cost brought by gradient surgery, we propose an implicit gradient surgery method, which approximates the solution to the aforementioned constrained optimization problem via only one backpropagation, thereby achieving efficient utility-preserving MU. Theoretically, we provide a tight convergence analysis of the algorithm. Empirically, our extensive experiments show that the proposed algorithm achieves better tradeoff results than existing baselines. Codes are available at https://github.com/anseryuer/EUPMU-Efficient-Utility-Preserving-Machine-Unlearning.

翻译：机器遗忘（MU）旨在从预训练模型中高效移除敏感或有害的记忆。其核心挑战在于平衡遗忘效能与效用保持之间的潜在权衡，即在按定义遗忘不良信息的同时维持模型的原始性能。解决该问题的一种潜在途径是采用多目标优化方法，联合优化遗忘目标与效用保持目标。然而，现有的多目标方法仅能保证找到帕累托最优解而缺乏细粒度控制，这导致遗忘目标优化不足。为此，我们首先将MU建模为一个约束优化问题，即在效用损失有界增加的约束下优化遗忘目标。随后，我们证明求解该优化问题等价于对遗忘目标实施单边梯度手术。为消除梯度手术带来的额外计算开销，我们提出一种隐式梯度手术方法，该方法仅通过一次反向传播即可近似求解上述约束优化问题，从而实现高效保持效用的MU。理论上，我们提供了该算法的严格收敛性分析。实证方面，我们的大量实验表明，所提算法相比现有基线取得了更优的权衡结果。代码发布于 https://github.com/anseryuer/EUPMU-Efficient-Utility-Preserving-Machine-Unlearning。