Balancing Act: Constraining Disparate Impact in Sparse Models

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each subgroup. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups. Current deep learning practice displays a trend towards larger architectures (Bommasani et al., 2021), as exemplified by popular models such as GPT-4 (OpenAI, 2023), Llama 2 (Touvron et al., 2023) and DALL-E 2 (Ramesh et al., 2022). Model compression techniques such as pruning (Gale et al., 2019), knowledge distillation (Hinton et al., 2015), or quantization (Gholami et al., 2021) are crucial towards enabling the deployment of large models across a wide range of platforms, including resource-constrained edge devices like smartphones. Despite achieving comparable performance at an aggregate level over the entire dataset, pruned models often exhibit significant accuracy reduction for some data sub-groups (Hooker et al., 2019; 2020; Paganini, 2020). In particular, under-represented groups can suffer high performance degradation while the overall performance remains unaffected, thus exacerbating systemic biases in machine learning models. Tran et al. (2022) refer to this phenomenon as the disparate impact of pruning. Existing mitigation methods face challenges in terms of interpretability and scalability to a large number of sub-groups. Tran et al. (2022) introduce constraints aiming to equalize the loss of the sparse model across sub-groups. However, their approach does not account for the unequal grouplevel performance of the dense model. Moreover, while the loss can be a useful surrogate for training, this method addresses the disparate impact issue indirectly as it focuses on controlling the loss, rather than group-level changes in accuracy. Alternatively, Lin et al. (2022) compute per-group importance scores for every model parameter to determine the weights to be pruned. This approach becomes prohibitively expensive when the model or the number of sub-groups is large.