Optimization layers in deep neural networks have enjoyed a growing popularity
in structured learning, improving the state of the art on a variety of
applications. Yet, these pipelines lack interpretability since they are made of
two opaque layers: a highly non-linear prediction model, such as a deep neural
network, and an optimization layer, which is typically a complex black-box
solver. Our goal is to improve the transparency of such methods by providing
counterfactual explanations. We build upon variational autoencoders a
principled way of obtaining counterfactuals: working in the latent space leads
to a natural notion of plausibility of explanations. We finally introduce a
variant of the classic loss for VAE training that improves their performance in
our specific structured context. These provide the foundations of CF-OPT, a
first-order optimization algorithm that can find counterfactual explanations
for a broad class of structured learning architectures. Our numerical results
show that both close and plausible explanations can be obtained for problems
from the recent literature.

通过变分自动编码器在深度学习模型中释放潜在空间的潜力，提出了一种改进的损失函数用于解释非结构化学习架构中的反事实情况，并展示了该方法在近期文献的问题上的有效性。