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

arXiv: https://arxiv.org/abs/2307.08964 · HTML: https://mlsanity.com/paper/2307.08964/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 20 of 20)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [BOME! Bilevel Optimization Made Easy: A Simple First-Order Approach](https://mlsanity.com/paper/2209.08709/) (2022)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [End to end learning and optimization on graphs](https://mlsanity.com/paper/1905.13732/) (2019)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problems](https://mlsanity.com/paper/2210.12547/) (2022)
- [Branch & Learn for Recursively and Iteratively Solvable Problems in Predict+Optimize](https://mlsanity.com/paper/2205.01672/) (2022)

## Built on by (most cited first, 18 of 18)

- [AdvPrompter: Fast Adaptive Adversarial Prompting for LLMs](https://mlsanity.com/paper/2404.16873/) (2024)
- [Decision-Focused Learning with Directional Gradients](https://mlsanity.com/paper/2402.03256/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [TaskMet: Task-Driven Metric Learning for Model Learning](https://mlsanity.com/paper/2312.05250/) (2023)
- [BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learning](https://mlsanity.com/paper/2411.19285/) (2024)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [Decision-Focused Fine-Tuning of Time Series Foundation Models for Dispatchable Feeder Optimization](https://mlsanity.com/paper/2503.01936/) (2025)
- [DF2: Distribution-Free Decision-Focused Learning](https://mlsanity.com/paper/2308.05889/) (2023)
- [GenCO: Generating Diverse Designs with Combinatorial Constraints](https://mlsanity.com/paper/2310.02442/) (2023)
- [Learning Joint Models of Prediction and Optimization](https://mlsanity.com/paper/2409.04898/) (2024)
- [A Solver-Free Training Method for Predict-then-Optimize](https://mlsanity.com/paper/2606.19587/) (2026)
- [Bi-Level Decision-Focused Causal Learning for Large-Scale Marketing Optimization: Bridging Observational and Experimental Data](https://mlsanity.com/paper/2510.19517/) (2025)
- [Decision-Focused Learning Enhanced by Automated Feature Engineering for Energy Storage Optimisation](https://mlsanity.com/paper/2509.05772/) (2025)
- [Contextual Scenario Generation for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2502.05349/) (2025)
- [Scalable Decision Focused Learning via Online Trainable Surrogates](https://mlsanity.com/paper/2512.03861/) (2025)
- [PolyStepOR: Learning to Decide Without Optimal Decisions](https://mlsanity.com/paper/2609.32465/) (2026)
- [FLAT: Smoothing the Rugged Landscape for Learnable, Sample-Efficient Traffic Calibration](https://mlsanity.com/paper/2610.04337/) (2026)

## Abstract (arXiv)

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 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 fcirc 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 g during both training and testing. The training is further challenged by sparse gradients of g, especially for combinatorial solvers. To address these challenges, we propose using a smooth and learnable Landscape Surrogate M as a replacement for fcirc g. This surrogate, learnable by neural networks, can be computed faster than the solver 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 g. Notably, our approach outperforms existing methods for computationally expensive high-dimensional problems.