Deep neural networks have demonstrated remarkable performance in various tasks. With a growing need for sparse deep learning, model compression techniques, especially pruning, have gained significant attention. However, conventional pruning techniques can inadvertently exacerbate algorithmic bias, resulting in unequal predictions. To address this, we define a fair pruning task where a sparse model is derived subject to fairness requirements. In particular, we propose a framework to jointly optimize the pruning mask and weight update processes with fairness constraints. This framework is engineered to compress models that maintain performance while ensuring fairness in a single execution. To this end, we formulate the fair pruning problem as a novel constrained bi-level optimization task and derive efficient and effective solving strategies. We design experiments spanning various datasets and settings to validate our proposed method. Our empirical analysis contrasts our framework with several mainstream pruning strategies, emphasizing our method's superiority in maintaining model fairness, performance, and efficiency.

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