  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.
