Optimizing Neural Networks with Gradient Lexicase Selection

One potential drawback of using aggregated performance measurement in machine learning is that models may learn to accept higher errors on some training cases as compromises for lower errors on others, with the lower errors actually being instances of overfitting. This can lead to both stagnation at local optima and poor generalization. Lexicase selection is an uncompromising method developed in evolutionary computation, which selects models on the basis of sequences of individual training case errors instead of using aggregated metrics such as loss and accuracy. In this paper, we investigate how lexicase selection, in its general form, can be integrated into the context of deep learning to enhance generalization. We propose Gradient Lexicase Selection, an optimization framework that combines gradient descent and lexicase selection in an evolutionary fashion. Our experimental results demonstrate that the proposed method improves the generalization performance of various widely-used deep neural network architectures across three image classification benchmarks. Additionally, qualitative analysis suggests that our method assists networks in learning more diverse representations. Modern data-driven learning algorithms, in general, define an optimization objective, e.g., a fitness function for parent selection in genetic algorithms (Holland, 1992) or a loss function for gradient descent in deep learning (LeCun et al., 2015), which computes the aggregate performance on the training data to guide the optimization process. Taking the image classification problem as an example, most recent approaches use Cross-Entropy loss with gradient descent (Bottou, 2010) and backpropagation (Rumelhart et al., 1985) to train deep neural networks (DNNs) on batches of training images. Despite the success that advanced DNNs can reach human-level performance on the image recognition task (Russakovsky et al., 2015), one potential drawback for such aggregated performance measurement is that the model may learn to seek "compromises" during the learning procedure, e.g., optimizing model weights to intentionally keep some errors in order to gain higher likelihood on correct predictions.