Many real-world problems can be efficiently modeled as Mixed Integer Programs
(MIPs) and solved with the Branch-and-Bound method. Prior work has shown the
existence of MIP backdoors, small sets of variables such that prioritizing
branching on them when possible leads to faster running times. However, finding
high-quality backdoors that improve running times remains an open question.
Previous work learns to estimate the relative solver speed of randomly sampled
backdoors through ranking and then decide whether to use it. In this paper, we
utilize the Monte-Carlo tree search method to collect backdoors for training,
rather than relying on random sampling, and adapt a contrastive learning
framework to train a Graph Attention Network model to predict backdoors. Our
method, evaluated on four common MIP problem domains, demonstrates performance
improvements over both Gurobi and previous models.

利用蒙特卡洛树搜索方法收集训练数据，通过对比学习框架训练图注意力网络模型来预测 Mixed Integer Programs 中的 MIP backdoors，相比 Gurobi 和之前的模型，在四个常见的 MIP 问题领域中展现了性能的提升。

利用对比学习学习混合整数规划问题的后门

Learning Backdoors for Mixed Integer Programs with Contrastive Learning

Solving partially observable Markov decision processes (POMDPs) is highly
intractable in general, at least in part because the optimal policy may be
infinitely large. In this paper, we explore the problem of finding the optimal
policy from a restricted set of policies, represented as finite state automata
of a given size. This problem is also intractable, but we show that the
complexity can be greatly reduced when the POMDP and/or policy are further
constrained. We demonstrate good empirical results with a branch-and-bound
method for finding globally optimal deterministic policies, and a
gradient-ascent method for finding locally optimal stochastic policies.

本文研究部分可观察马尔可夫决策过程（POMDPs）的解决方案，探讨如何从有限状态自动机的限制集合中找到最佳策略，进而展示了通过分支定界法和梯度上升法寻找全局最优确定性策略和局部最优随机策略的优越实验结果。