We propose a self-supervised learning approach for solving the following constrained optimization task in log-linear models or Markov networks. Let $f$ and $g$ be two log-linear models defined over the sets $\mathbf{X}$ and $\mathbf{Y}$ of random variables respectively. Given an assignment $\mathbf{x}$ to all variables in $\mathbf{X}$ (evidence) and a real number $q$, the constrained most-probable explanation (CMPE) task seeks to find an assignment $\mathbf{y}$ to all variables in $\mathbf{Y}$ such that $f(\mathbf{x}, \mathbf{y})$ is maximized and $g(\mathbf{x}, \mathbf{y})\leq q$. In our proposed self-supervised approach, given assignments $\mathbf{x}$ to $\mathbf{X}$ (data), we train a deep neural network that learns to output near-optimal solutions to the CMPE problem without requiring access to any pre-computed solutions. The key idea in our approach is to use first principles and approximate inference methods for CMPE to derive novel loss functions that seek to push infeasible solutions towards feasible ones and feasible solutions towards optimal ones. We analyze the properties of our proposed method and experimentally demonstrate its efficacy on several benchmark problems.

翻译：我们提出了一种自监督学习方法，用于解决对数线性模型或马尔可夫网络中的以下约束优化任务。设$f$和$g$分别为定义在随机变量集$\mathbf{X}$和$\mathbf{Y}$上的两个对数线性模型。给定对$\mathbf{X}$中所有变量的赋值$\mathbf{x}$（证据）和一个实数$q$，约束最可能解释（CMPE）任务旨在寻找对$\mathbf{Y}$中所有变量的赋值$\mathbf{y}$，使得$f(\mathbf{x}, \mathbf{y})$最大化且$g(\mathbf{x}, \mathbf{y})\leq q$。在我们提出的自监督方法中，给定对$\mathbf{X}$的赋值$\mathbf{x}$（数据），我们训练一个深度神经网络，使其能够学习输出CMPE问题的近最优解，而无需访问任何预计算的解。该方法的核心思想是利用CMPE的基本原理和近似推理方法，推导出新颖的损失函数，这些损失函数旨在将不可行解推向可行解，并将可行解推向最优解。我们分析了所提出方法的性质，并通过多个基准问题实验验证了其有效性。