Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approach

TL;DR

The paper tackles the computational bottleneck in end-to-end decision-focused learning by introducing ProjectNet, a meta-optimization framework that learns fast surrogate optimization updates with differentiable, feasibility-preserving projections. It provides analytical guarantees on convergence and generalization and demonstrates applicability to both single-stage and two-stage stochastic problems across electricity planning, shortest-path, and newsvendor settings. Empirically, ProjectNet achieves competitive or better decision quality while delivering substantial training-time savings compared with traditional predict-then-optimize and existing end-to-end baselines, and it scales favorably with problem size. The work delivers practical end-to-end learning tools that maintain feasibility, improve efficiency, and extend to complex multi-stage decision problems, with broad potential impact on industrial optimization pipelines.

Abstract

End-to-end learning has become a widely applicable and studied problem in training predictive ML models to be aware of their impact on downstream decision-making tasks. These end-to-end models often outperform traditional methods that separate training from the optimization and only myopically focus on prediction error. However, the computational complexity of end-to-end frameworks poses a significant challenge, particularly for large-scale problems. While training an ML model using gradient descent, each time we need to compute a gradient we must solve an expensive optimization problem. We present a meta-optimization method that learns efficient algorithms to approximate optimization problems, dramatically reducing computational overhead of solving the decision problem in general, an aspect we leverage in the training within the end-to-end framework. Our approach introduces a neural network architecture that near-optimally solves optimization problems while ensuring feasibility constraints through alternate projections. We prove exponential convergence, approximation guarantees, and generalization bounds for our learning method. This method offers superior computational efficiency, producing high-quality approximations faster and scaling better with problem size compared to existing techniques. Our approach applies to a wide range of optimization problems including deterministic, single-stage as well as two-stage stochastic optimization problems. We illustrate how our proposed method applies to (1) an electricity generation problem using real data from an electricity routing company coordinating the movement of electricity throughout 13 states, (2) a shortest path problem with a computer vision task of predicting edge costs from terrain maps, (3) a two-stage multi-warehouse cross-fulfillment newsvendor problem, as well as a variety of other newsvendor-like problems.

Figures (13)

• Figure 1: Lower mean-squared error in prediction does not imply lower objective value of the corresponding decisions.
• Figure 2: Flow diagram for end-to-end learning using ProjectNet.
• Figure 3: Iterative projection method. The sequence of projections converges to a feasible solution (depicted as the blue point).
• Figure 4: ProjectNet architecture
• Figure 5: Comparison of ProjectNet to Gradient Descent

Theorems & Definitions (14)

• Theorem 1: Approximation impact on end-to-end
• proof
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Definition 1: Multidimensional Rademacher Complexity
• Theorem 2: Generalization bound