Mixed Integer programs (MIPs) are typically solved by the Branch-and-Bound algorithm. Recently, Learning to imitate fast approximations of the expert strong branching heuristic has gained attention due to its success in reducing the running time for solving MIPs. However, existing learning-to-branch methods assume that the entire training data is available in a single session of training. This assumption is often not true, and if the training data is supplied in continual fashion over time, existing techniques suffer from catastrophic forgetting. In this work, we study the hitherto unexplored paradigm of Lifelong Learning to Branch on Mixed Integer Programs. To mitigate catastrophic forgetting, we propose LIMIP, which is powered by the idea of modeling an MIP instance in the form of a bipartite graph, which we map to an embedding space using a bipartite Graph Attention Network. This rich embedding space avoids catastrophic forgetting through the application of knowledge distillation and elastic weight consolidation, wherein we learn the parameters key towards retaining efficacy and are therefore protected from significant drift. We evaluate LIMIP on a series of NP-hard problems and establish that in comparison to existing baselines, LIMIP is up to 50% better when confronted with lifelong learning.

翻译：混合整数规划（MIP）通常通过分支定界算法求解。近年来，通过学习来模仿专家强分支启发式的快速近似方法因其在减少MIP求解运行时间方面的成功而受到关注。然而，现有的学习分支方法假设全部训练数据可在单次训练会话中获取。这种假设往往不成立，若训练数据以持续方式随时间提供，现有技术将遭受灾难性遗忘。本研究探索了此前未涉足的混合整数规划终身学习范式。为缓解灾难性遗忘，我们提出LIMIP方法，其核心思想是将MIP实例建模为二分图，并通过二分图注意力网络将其映射至嵌入空间。该丰富的嵌入空间通过知识蒸馏和弹性权重巩固避免了灾难性遗忘——在此过程中我们学习对保持效能至关重要的参数，从而防止其发生显著漂移。我们在系列NP难问题上评估LIMIP，结果表明，相较于现有基线方法，LIMIP在面对终身学习时性能提升高达50%。