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

Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information