面向多层级预算组合问题的课程学习
Curriculum learning for multilevel budgeted combinatorial problems
AI总结：
针对图上两人零和的多层级预算组合优化问题，提出基于价值的多智能体强化学习与预算递增课程训练方法，在百节点图上接近最优，并较最快精确求解器平均加速185倍。
摘要：
通过图神经网络学习组合优化问题的启发式方法，近来已在若干经典NP难问题上展现出良好结果。这些问题是只有一个参与者的单层级优化问题。多层级组合优化问题是其推广，涵盖多个参与者依次决策的情形。通过将其置于多智能体强化学习设定中，我们设计了一种基于价值的方法，以学习求解涉及两个参与者在图上进行零和博弈的多层级预算组合问题。我们的框架基于一种简单课程：如果智能体知道如何估计预算不超过$B$的实例价值，那么无论优化方向如何，都可通过检查每个可能后继状态的价值，在多项式时间内求解预算为$B+1$的实例。因此，我们以自底向上的方式生成由启发式求解、预算逐渐增大的实例数据集来训练智能体。我们报告：在最多$100$个节点的图上取得接近最优的结果；并且相对于Multilevel Critical Node问题已知最快的精确求解器，平均实现$185\times$加速；该问题是一个max-min-max三层级问题，已被证明至少为$\Sigma_2^p$-hard。
英文摘要：
Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel combinatorial optimization problems are their generalization, encompassing situations with multiple players taking decisions sequentially. By framing them in a multi-agent reinforcement learning setting, we devise a value-based method to learn to solve multilevel budgeted combinatorial problems involving two players in a zero-sum game over a graph. Our framework is based on a simple curriculum: if an agent knows how to estimate the value of instances with budgets up to $B$, then solving instances with budget $B+1$ can be done in polynomial time regardless of the direction of the optimization by checking the value of every possible afterstate. Thus, in a bottom-up approach, we generate datasets of heuristically solved instances with increasingly larger budgets to train our agent. We report results close to optimality on graphs up to $100$ nodes and a $185 \times$ speedup on average compared to the quickest exact solver known for the Multilevel Critical Node problem, a max-min-max trilevel problem that has been shown to be at least $Σ_2^p$-hard.
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。
