[Paper Review] A Survey of Contextual Optimization Methods for Decision Making under Uncertainty

Utsav Sadana, Abhilash Chenreddy+4 more|arXiv (Cornell University)|Jun 17, 2023

Forecasting Techniques and Applications16 citations

TL;DR

A comprehensive survey of contextual optimization, detailing three learning-and-optimization frameworks (decision rule optimization, sequential learning and optimization, and integrated learning and optimization) and their models, training methods, and theoretical guarantees.

ABSTRACT

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming.

Motivation & Objective

• Clarify how side information (covariates) is used to inform decisions under uncertainty.
• Unify notation and terminology across decision rule optimization, sequential learning and optimization, and integrated learning and optimization.
• Summarize models, training procedures, and theoretical guarantees across the literature.
• Highlight open questions and directions for integrating ML with stochastic optimization.

Proposed method

• Define contextual optimization problems with covariates and uncertain parameters.
• Present three learning paradigms: decision rule optimization, sequential learning and optimization (SLO), and integrated learning and optimization (ILO).
• Review linear, RKHS-based, and non-linear decision rules within the decision-rule framework.
• Discuss distributionally robust and surrogate/ differentiable training approaches within ILO.
• Explain training via unrolling, implicit differentiation, and differentiable surrogates (e.g., SPO+).
• Summarize connections to related paradigms like policy optimization and end-to-end learning.

Experimental results

Research questions

• RQ1 What are the main frameworks for learning policies in contextual optimization and how do they differ?
• RQ2 How do different decision rules (linear, RKHS, non-linear) perform under contextual information?
• RQ3 What training paradigms best align predictive models with downstream optimization objectives?
• RQ4 What theoretical guarantees exist for these contextual optimization methods, including robustness and consistency?
• RQ5 Where are the open theoretical and algorithmic challenges in integrating ML with stochastic programming?

Key findings

• Three main frameworks are identified: decision rule optimization, sequential learning and optimization (SLO), and integrated learning and optimization (ILO).
• RKHS-based and non-linear decision rules can extend beyond linear policies and achieve asymptotic optimality in some settings.
• Integrated learning emphasizes optimizing predictive models directly for prescriptive performance rather than solely predictive accuracy.
• Distributionally robust and Wasserstein-based approaches are explored to guard against model misspecification and data shifts.
• The survey connects frameworks to related lines of work such as regret minimization and end-to-end learning, and discusses training via unrolling and implicit differentiation.