# Dynamic optimization with side information

arXiv: https://arxiv.org/abs/1907.07307 · HTML: https://mlsanity.com/paper/1907.07307/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2019.

## Built on by (most cited first, 14 of 14)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Distributionally Robust Optimal Power Flow with Contextual Information](https://mlsanity.com/paper/2109.07896/) (2021)
- [Decision-Focused Forecasting: A Differentiable Multistage Optimisation Architecture](https://mlsanity.com/paper/2405.14719/) (2024)
- [Multistage Stochastic Optimization via Kernels](https://mlsanity.com/paper/2303.06515/) (2023)
- [Contextual Stochastic Vehicle Routing with Time Windows](https://mlsanity.com/paper/2402.06968/) (2024)
- [Epistemic Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2604.07072/) (2026)
- ["Over-optimizing" for Normality: Budget-constrained Uncertainty Quantification for Contextual Decision-making](https://mlsanity.com/paper/2503.12747/) (2025)
- [Prescribe-then-Select: Adaptive Policy Selection for Contextual Stochastic Optimization](https://mlsanity.com/paper/2509.08194/) (2025)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)
- [Deployment of AI-Assisted Interventions: Capacity Constraints and Noisy Compliance](https://mlsanity.com/paper/2604.14370/) (2026)
- [Smooth Learning with Hard Constraints via Legendre-Regularized Policies](https://mlsanity.com/paper/2607.24007/) (2026)

## Abstract (arXiv)

We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of various data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concentration result for a class of machine learning methods, we prove that the proposed approach is asymptotically optimal for multi-period stochastic programming with side information. We also describe a general-purpose approximation for these optimization problems, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with many stages. Across a variety of examples in inventory management, finance, and shipment planning, our method achieves improvements of up to 15% over alternatives and requires less than one minute of computation time on problems with twelve stages.