Data-driven algorithm design is a paradigm that uses statistical and machine
learning techniques to select from a class of algorithms for a computational
problem an algorithm that has the best expected performance with respect to
some (unknown) distribution on the instances of the problem. We build upon
recent work in this line of research by introducing the idea where, instead of
selecting a single algorithm that has the best performance, we allow the
possibility of selecting an algorithm based on the instance to be solved. In
particular, given a representative sample of instances, we learn a neural
network that maps an instance of the problem to the most appropriate algorithm
{\em for that instance}. We formalize this idea and derive rigorous sample
complexity bounds for this learning problem, in the spirit of recent work in
data-driven algorithm design. We then apply this approach to the problem of
making good decisions in the branch-and-cut framework for mixed-integer
optimization (e.g., which cut to add?). In other words, the neural network will
take as input a mixed-integer optimization instance and output a decision that
will result in a small branch-and-cut tree for that instance. Our computational
results provide evidence that our particular way of using neural networks for
cut selection can make a significant impact in reducing branch-and-cut tree
sizes, compared to previous data-driven approaches.

数据驱动算法设计通过使用统计和机器学习技术，从一个算法类中选择一个在某个（未知）分布中期望表现最佳的算法。该论文提出了一种在解决问题时可以基于问题实例选择算法的思想，并应用于混合整数优化的分支切割框架中，通过神经网络在决策中起到重要作用。

基于数据驱动的神经网络算法设计及其在分支定界中的应用

Data-driven algorithm design using neural networks with applications to  branch-and-cut

Data-driven algorithm design, that is, choosing the best algorithm for a
specific application, is a crucial problem in modern data science.
Practitioners often optimize over a parameterized algorithm family, tuning
parameters based on problems from their domain. These procedures have
historically come with no guarantees, though a recent line of work studies
algorithm selection from a theoretical perspective. We advance the foundations
of this field in several directions: we analyze online algorithm selection,
where problems arrive one-by-one and the goal is to minimize regret, and
private algorithm selection, where the goal is to find good parameters over a
set of problems without revealing sensitive information contained therein. We
study important algorithm families, including SDP-rounding schemes for problems
formulated as integer quadratic programs, and greedy techniques for canonical
subset selection problems. In these cases, the algorithm's performance is a
volatile and piecewise Lipschitz function of its parameters, since tweaking the
parameters can completely change the algorithm's behavior. We give a sufficient
and general condition, dispersion, defining a family of piecewise Lipschitz
functions that can be optimized online and privately, which includes the
functions measuring the performance of the algorithms we study. Intuitively, a
set of piecewise Lipschitz functions is dispersed if no small region contains
many of the functions' discontinuities. We present general techniques for
online and private optimization of the sum of dispersed piecewise Lipschitz
functions. We improve over the best-known regret bounds for a variety of
problems, prove regret bounds for problems not previously studied, and give
matching lower bounds. We also give matching upper and lower bounds on the
utility loss due to privacy. Moreover, we uncover dispersion in auction design
and pricing problems.

探索了数据驱动的算法设计中的在线选择算法和隐私保护算法选择问题，提出了分散条件以优化这些问题的解决方案。