Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedback
Proposed a decision-focused on-policy learning method for contextual linear optimization with partial feedback, showing lower cumulative regret than baselines.
Key Findings
Methodology
The method employs a hybrid gradient estimator, combining an unbiased score function estimator and a decision-focused plug-in component. It updates the distributional model by sampling cost-vector predictions from a conditional distribution and solving the downstream linear optimization problem.
Key Results
- Experiments show lower cumulative regret on benchmarks like top-k selection, shortest path, combinatorial pricing, and energy scheduling compared to contextual bandit baselines.
- Using Gaussian and richer conditional generative models, the hybrid gradient approach outperforms across all benchmarks.
- Proved an O(T^{-1/2}) bound on the average squared policy-gradient norm, matching the standard non-convex SGD rate.
Significance
This study is significant for academia and industry, addressing challenges in contextual linear optimization with partial feedback. It enhances decision systems by optimizing downstream decision quality rather than standalone prediction accuracy.
Technical Contribution
Technical contributions include introducing new on-policy stochastic gradient estimators combining score function and decision-focused plug-in, offering new theoretical guarantees and engineering possibilities.
Novelty
This method is the first to apply decision-focused learning to on-policy contextual linear optimization, particularly in partial feedback environments, offering an innovative hybrid gradient estimation approach.
Limitations
- In high-dimensional spaces, score function estimation may lead to high variance issues.
- The performance of the plug-in component depends on the accuracy of the auxiliary estimate.
Future Work
Future work could explore more complex feedback structures and more efficient distribution model update methods.
AI Executive Summary
In many operational systems, decisions are made by solving constrained optimization problems. However, traditional methods often rely on offline data and full observations of the objective cost vector, which is often impractical in real applications.
This paper proposes a novel decision-focused on-policy learning method for contextual linear optimization with partial feedback. The method updates policy parameters by sampling cost-vector predictions from a conditional distribution and solving the downstream linear optimization problem. Experiments show that this method outperforms existing contextual bandit methods across multiple benchmarks.
Despite its strong performance in experiments, the method has limitations, such as high variance issues in high-dimensional spaces. Future research could further optimize distribution model update methods to improve efficiency and accuracy.
Deep Analysis
Background
Decision-focused learning trains predictive models by optimizing downstream decision quality rather than standalone prediction accuracy. Contextual linear optimization has broad applications in fields like vehicle routing and dynamic pricing.
Core Problem
Traditional methods assume offline data and full observations of the objective cost vector, which is often impractical in real applications. Contextual linear optimization with partial feedback is a challenge.
Innovation
This paper introduces a new on-policy learning method combining score function and decision-focused plug-in components, effectively updating policy parameters in partial feedback environments.
Methodology
- �� Uses a hybrid gradient estimator combining score function and plug-in components.
- �� Samples cost-vector predictions from a conditional distribution.
- �� Solves downstream linear optimization problems to update policy parameters.
Experiments
Experiments are conducted on top-k selection, shortest path, combinatorial pricing, and energy scheduling benchmarks using Gaussian and richer conditional generative models.
Results
Results show lower cumulative regret across all benchmarks compared to contextual bandit baselines, with an O(T^{-1/2}) policy gradient norm bound.
Applications
The method can be applied in fields requiring contextual linear optimization, such as logistics, energy management, and dynamic pricing.
Limitations & Outlook
Score function estimation in high-dimensional spaces may lead to high variance issues, and the plug-in component's performance depends on the accuracy of the auxiliary estimate.
Plain Language Accessible to non-experts
Imagine you're cooking in a kitchen. You need to make the best choice based on the price and quality of ingredients, but you can only see partial price information. This method acts like a smart assistant that can guess the most likely prices based on the limited information you provide and help you make the best decision.
ELI14 Explained like you're 14
Imagine you're playing a game where you need to choose the best path to get the highest score, but you can only see part of the map. This method is like a super-smart game assistant that can guess the hidden parts of the map based on what you see and help you choose the best path!
Glossary
Decision-Focused Learning
A method that trains models by optimizing downstream decision quality rather than standalone prediction accuracy.
Used to train predictive models to enhance decision system efficiency.
Contextual Linear Optimization
The process of solving linear optimization problems given contextual information.
Used for online learning in partial feedback environments.
Partial Feedback
A feedback mechanism where only partial information is observed during decision-making.
The feedback environment considered in the study.
Hybrid Gradient Estimation
A gradient estimation method combining score function and decision-focused plug-in.
Used for updating policy parameters.
Score Function Estimation
An unbiased policy gradient estimation method that may lead to high variance.
A component in hybrid gradient estimation.
Open Questions Unanswered questions from this research
- 1 How to effectively reduce the variance of score function estimation in high-dimensional spaces?
- 2 How to improve the performance of the plug-in component under different feedback structures?
Applications
Immediate Applications
Logistics Optimization
Can be used to optimize logistics route selection, improving transportation efficiency.
Long-term Vision
Smart Energy Management
Optimizes energy scheduling to improve energy utilization and reduce costs.
Abstract
Decision-focused learning (DFL) trains predictive models by optimizing downstream decision quality rather than standalone prediction accuracy. For contextual linear optimization, most existing DFL methods assume offline data and full observations of the objective cost vector. We develop an on-policy learning method for sequential contextual linear optimization under partial feedback, generalizing the standard bandit feedback setting. Our method learns a stochastic predict-then-optimize policy that samples a cost-vector prediction from a conditional distribution and solves the resulting downstream linear optimization problem. To update this distributional model, we introduce a two-component hybrid gradient estimator. The first component is a score function estimator, which provides an unbiased but potentially high-variance policy gradient estimate. The second is a decision-focused plug-in component that uses an auxiliary nuisance estimate of the latent cost vector to exploit the downstream optimization structure, becoming more informative as the estimate improves. We prove an $\mathcal{O}(T^{-1/2})$ bound on the average squared policy-gradient norm, matching the standard non-convex SGD rate. Experiments on top-$k$ selection, shortest path, combinatorial pricing, and a real-data energy-scheduling benchmark show that the hybrid gradient approach achieves lower cumulative regret than contextual-bandit-style baselines across all benchmarks, using both Gaussian and richer conditional generative models. Code is available at https://github.com/Joeyetinghan/on-policy-bandit-dfl.