提升凸二次规划
Lifted Convex Quadratic Programming
摘要：
对称性是提升推理的基本要素，最近已经证明了在高度连接但对称的概率模型中执行非常有效的推理的可能性。这就提出了一个问题，这是否适用于一般的优化问题。在这里，我们表明，对于一大类优化方法，这实际上是这种情况。更确切地说，我们引入了凸二次规划（QP）的分数对称性的概念，这是许多机器学习方法的核心，并利用它来提升，即，来压缩QP。这些提升的QP然后可以用通常的优化工具箱（现成的求解器、切割平面算法、随机梯度等）来处理。如果原始QP表现出对称性，则提升的QP通常将更紧凑，因此它们的优化可能更有效。
英文摘要：
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether this holds for optimisation problems in general. Here we show that for a large class of optimisation methods this is actually the case. More precisely, we introduce the concept of fractional symmetries of convex quadratic programs (QPs), which lie at the heart of many machine learning approaches, and exploit it to lift, i.e., to compress QPs. These lifted QPs can then be tackled with the usual optimization toolbox (off-the-shelf solvers, cutting plane algorithms, stochastic gradients etc.). If the original QP exhibits symmetry, then the lifted one will generally be more compact, and hence their optimization is likely to be more efficient.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
