Many real-world decision processes are modeled by optimization problems whose
defining parameters are unknown and must be inferred from observable data. The
Predict-Then-Optimize framework uses machine learning models to predict unknown
parameters of an optimization problem from features before solving. Recent
works show that decision quality can be improved in this setting by solving and
differentiating the optimization problem in the training loop, enabling
end-to-end training with loss functions defined directly on the resulting
decisions. However, this approach can be inefficient and requires handcrafted,
problem-specific rules for backpropagation through the optimization step. This
paper proposes an alternative method, in which optimal solutions are learned
directly from the observable features by predictive models. The approach is
generic, and based on an adaptation of the Learning-to-Optimize paradigm, from
which a rich variety of existing techniques can be employed. Experimental
evaluations show the ability of several Learning-to-Optimize methods to provide
efficient, accurate, and flexible solutions to an array of challenging
Predict-Then-Optimize problems.

从观测特征中通过预测模型直接学习最优解的方法被提出，该方法是泛化的，基于学习优化范式，能够提供高效、准确和灵活的解决方案给一系列具有挑战性的预测优化问题。

代理预测优化：学习预测和优化的联合模型

Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and  Optimization

This paper presents a learning-based method for multi-view depth estimation
from posed images. Our core idea is a "learning-to-optimize" paradigm that
iteratively indexes a plane-sweeping cost volume and regresses the depth map
via a convolutional Gated Recurrent Unit (GRU). Since the cost volume plays a
paramount role in encoding the multi-view geometry, we aim to improve its
construction both at pixel- and frame- levels. At the pixel level, we propose
to break the symmetry of the Siamese network (which is typically used in MVS to
extract image features) by introducing a transformer block to the reference
image (but not to the source images). Such an asymmetric volume allows the
network to extract global features from the reference image to predict its
depth map. Given potential inaccuracies in the poses between reference and
source images, we propose to incorporate a residual pose network to correct the
relative poses. This essentially rectifies the cost volume at the frame level.
We conduct extensive experiments on real-world MVS datasets and show that our
method achieves state-of-the-art performance in terms of both within-dataset
evaluation and cross-dataset generalization.

本文提出了一种基于学习的方法，通过迭代索引平面扫描成本体积并借助卷积门控循环单元来回归深度图，从而进行多视角深度估计。经过对真实世界多视图数据集的大量实验，验证了该方法在数据集内部性能和跨数据集概括性能方面都达到了最先进水平。