  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.
