从上下文示例学习混合线性规划
Learning Mixed-Integer Linear Programs from Contextual Examples
摘要：
混合整数线性规划（MILP）广泛应用于人工智能和运筹学中，用于模拟调度和路由等复杂决策问题。然而，设计这样的程序需要领域和建模专业知识。在本文中，我们研究的问题，从上下文的例子，一个新颖的和现实的设置，其中的例子捕获的解决方案和非解决方案在特定的上下文中获取MILP。由此产生的学习问题涉及获取连续参数-即成本向量和可行性多面体-但具有明显的组合风味。为了解决这个复杂的问题，我们还贡献MISSLE，从上下文的例子学习MILP的算法。MISSLE使用随机局部搜索的变体，其由连续替代损失函数的梯度引导。我们对合成数据的实证评估表明，MISSLE获得更好的MILP比基于随机局部搜索和梯度下降的替代品更快。
英文摘要：
Mixed-integer linear programs (MILPs) are widely used in artificial intelligence and operations research to model complex decision problems like scheduling and routing. Designing such programs however requires both domain and modelling expertise. In this paper, we study the problem of acquiring MILPs from contextual examples, a novel and realistic setting in which examples capture solutions and non-solutions within a specific context. The resulting learning problem involves acquiring continuous parameters -- namely, a cost vector and a feasibility polytope -- but has a distinctly combinatorial flavor. To solve this complex problem, we also contribute MISSLE, an algorithm for learning MILPs from contextual examples. MISSLE uses a variant of stochastic local search that is guided by the gradient of a continuous surrogate loss function. Our empirical evaluation on synthetic data shows that MISSLE acquires better MILPs faster than alternatives based on stochastic local search and gradient descent.
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