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Scalable Decision Focused Learning via Online Trainable Surrogates

Gaetano Signorelli, Michele Lombardi

TL;DR

This work tackles the scalability bottlenecks of Decision Focused Learning by introducing a Gaussian Process-based surrogate that replaces costly regret evaluations during training. The surrogate is trained online with stochastic smoothing and an optional sample-sharing mechanism, and it can switch to a fall-back method (SFGE) when confidence is low, preserving asymptotically unbiased gradient information. Empirical results across knapsack, set cover, and toy benchmarks show substantial reductions in inner solver calls and runtime without sacrificing solution quality, outperforming several black-box surrogate methods. The approach enhances applicability of DFL to complex, real-world problems with recourse and nonlinear costs, while maintaining scalability and robustness in high dimensions.

Abstract

Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to suboptimal solutions. Using the actual decision cost as a loss function (called Decision Focused Learning) can address this issue, but with a severe loss of scalability at training time. To address this issue, we propose an acceleration method based on replacing costly loss function evaluations with an efficient surrogate. Unlike previously defined surrogates, our approach relies on unbiased estimators reducing the risk of spurious local optima and can provide information on its local confidence allowing one to switch to a fallback method when needed. Furthermore, the surrogate is designed for a black-box setting, which enables compensating for simplifications in the optimization model and accounting for recourse actions during cost computation. In our results, the method reduces costly inner solver calls, with a solution quality comparable to other state-of-the-art techniques.

Scalable Decision Focused Learning via Online Trainable Surrogates

TL;DR

This work tackles the scalability bottlenecks of Decision Focused Learning by introducing a Gaussian Process-based surrogate that replaces costly regret evaluations during training. The surrogate is trained online with stochastic smoothing and an optional sample-sharing mechanism, and it can switch to a fall-back method (SFGE) when confidence is low, preserving asymptotically unbiased gradient information. Empirical results across knapsack, set cover, and toy benchmarks show substantial reductions in inner solver calls and runtime without sacrificing solution quality, outperforming several black-box surrogate methods. The approach enhances applicability of DFL to complex, real-world problems with recourse and nonlinear costs, while maintaining scalability and robustness in high dimensions.

Abstract

Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to suboptimal solutions. Using the actual decision cost as a loss function (called Decision Focused Learning) can address this issue, but with a severe loss of scalability at training time. To address this issue, we propose an acceleration method based on replacing costly loss function evaluations with an efficient surrogate. Unlike previously defined surrogates, our approach relies on unbiased estimators reducing the risk of spurious local optima and can provide information on its local confidence allowing one to switch to a fallback method when needed. Furthermore, the surrogate is designed for a black-box setting, which enables compensating for simplifications in the optimization model and accounting for recourse actions during cost computation. In our results, the method reduces costly inner solver calls, with a solution quality comparable to other state-of-the-art techniques.

Paper Structure

This paper contains 19 sections, 16 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Methodology
  5. Stochastic smoothing
  6. Sample sharing
  7. Algorithm
  8. Experiments
  9. Benchmarks
  10. Baselines
  11. Results
  12. Ablation studies
  13. Conclusions
  14. Conditions for the Effectiveness of the Classical DFL Setting
  15. Estimation Bias Analysis
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Illustration of stochastic smoothing with varying $\sigma$: larger values cause smoother functions with respect to the original regret loss. Smoothed functions are computed using importance sampling over a set of points sampled from Normal distributions.
  • Figure 2: Regret and solver calls across the benchmarks: points represent the average regret (on a logarithmic scale) and average solver calls per instance for all the baselines. Lines represent standard deviations for each method. Only the best (lowest regret) models are reported for LODL and EGL.