Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer $\mathbf{g}$ to tackle these challenging problems with $f$ as the objective, the optimization process can be substantially accelerated by leveraging past experience. The optimizer can be trained with supervision from known optimal solutions or implicitly by optimizing the compound function $f\circ \mathbf{g}$. The implicit approach may not require optimal solutions as labels and is capable of handling problem uncertainty; however, it is slow to train and deploy due to frequent calls to optimizer $\mathbf{g}$ during both training and testing. The training is further challenged by sparse gradients of $\mathbf{g}$, especially for combinatorial solvers. To address these challenges, we propose using a smooth and learnable Landscape Surrogate $M$ as a replacement for $f\circ \mathbf{g}$. This surrogate, learnable by neural networks, can be computed faster than the solver $\mathbf{g}$, provides dense and smooth gradients during training, can generalize to unseen optimization problems, and is efficiently learned via alternating optimization. We test our approach on both synthetic problems, including shortest path and multidimensional knapsack, and real-world problems such as portfolio optimization, achieving comparable or superior objective values compared to state-of-the-art baselines while reducing the number of calls to $\mathbf{g}$. Notably, our approach outperforms existing methods for computationally expensive high-dimensional problems.

翻译：近期在学习驱动优化领域的研究表明，当优化问题仅被部分观测或通用优化器在缺乏专家调参时表现不佳的情况下，该方法展现出潜力。通过以$f$为目标函数的学习型优化器$\mathbf{g}$解决这些挑战性问题，优化过程可利用过往经验实现显著加速。该优化器可通过已知最优解的监督训练，或隐式地优化复合函数$f\circ \mathbf{g}$进行训练。隐式方法无需将最优解作为标签，并能处理问题的不确定性，但其训练和部署过程因需频繁调用优化器$\mathbf{g}$而较为缓慢。此外，训练还面临$\mathbf{g}$梯度稀疏性的挑战（尤见于组合求解器）。为应对这些挑战，我们提出使用光滑且可学习的景观代理$M$替代$f\circ \mathbf{g}$。该代理可通过神经网络学习，相比求解器$\mathbf{g}$具有更快的计算速度，能在训练中提供密集且光滑的梯度，泛化至未见优化问题，并通过交替优化实现高效学习。我们在包括最短路径、多维背包在内的合成问题以及投资组合优化等真实问题上验证了该方法。与最先进基线相比，本方法在减少$\mathbf{g}$调用次数的同时，取得了相当或更优的目标函数值。值得注意的是，本方法在计算成本高昂的高维问题上表现优于现有方法。