Mathematical solvers use parametrized Optimization Problems (OPs) as inputs
to yield optimal decisions. In many real-world settings, some of these
parameters are unknown or uncertain. Recent research focuses on predicting the
value of these unknown parameters using available contextual features, aiming
to decrease decision regret by adopting end-to-end learning approaches.
However, these approaches disregard prediction uncertainty and therefore make
the mathematical solver susceptible to provide erroneous decisions in case of
low-confidence predictions. We propose a novel framework that models prediction
uncertainty with Bayesian Neural Networks (BNNs) and propagates this
uncertainty into the mathematical solver with a Stochastic Programming
technique. The differentiable nature of BNNs and differentiable mathematical
solvers allow for two different learning approaches: In the Decoupled learning
approach, we update the BNN weights to increase the quality of the predictions'
distribution of the OP parameters, while in the Combined learning approach, we
update the weights aiming to directly minimize the expected OP's cost function
in a stochastic end-to-end fashion. We do an extensive evaluation using
synthetic data with various noise properties and a real dataset, showing that
decisions regret are generally lower (better) with both proposed methods.

使用贝叶斯神经网络和随机规划技术的预测不确定性建模，以降低决策风险和提高决策质量。

基于贝叶斯神经网络的随机优化问题学习解决方案

Learning Solutions of Stochastic Optimization Problems with Bayesian  Neural Networks

We consider a suboptimal solution path algorithm for the Support Vector
Machine. The solution path algorithm is an effective tool for solving a
sequence of a parametrized optimization problems in machine learning. The path
of the solutions provided by this algorithm are very accurate and they satisfy
the optimality conditions more strictly than other SVM optimization algorithms.
In many machine learning application, however, this strict optimality is often
unnecessary, and it adversely affects the computational efficiency. Our
algorithm can generate the path of suboptimal solutions within an arbitrary
user-specified tolerance level. It allows us to control the trade-off between
the accuracy of the solution and the computational cost. Moreover, We also show
that our suboptimal solutions can be interpreted as the solution of a
\emph{perturbed optimization problem} from the original one. We provide some
theoretical analyses of our algorithm based on this novel interpretation. The
experimental results also demonstrate the effectiveness of our algorithm.

本文介绍了一种支持向量机的次优解路径算法，该算法可以在任意用户指定的容忍度范围内生成次优解路径，并能够控制解的准确性和计算成本的平衡。