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OPO: Making Decision-Focused Data Acquisition Decisions

Egon Peršak, Miguel F. Anjos

TL;DR

This work proposes a model for making data acquisition decisions for variables in contextual stochastic optimisation problems in which the acquisition of contextual variables is costly and consequently constrained and demonstrates that the differentiable optimisation approach outperforms random search strategies.

Abstract

We propose a model for making data acquisition decisions for variables in contextual stochastic optimisation problems. Data acquisition decisions are typically treated as separate and fixed. We explore problem settings in which the acquisition of contextual variables is costly and consequently constrained. The data acquisition problem is often solved heuristically for proxy objectives such as coverage. The more intuitive objective is the downstream decision quality as a result of data acquisition decisions. The whole pipeline can be characterised as an optimise-then-predict-then-optimise (OPO) problem. Analogously, much recent research has focused on how to integrate prediction and optimisation (PO) in the form of decision-focused learning. We propose leveraging differentiable optimisation to extend the integration to data acquisition. We solve the data acquisition problem with well-defined constraints by learning a surrogate linear objective function. We demonstrate an application of this model on a shortest path problem for which we first have to set a drone reconnaissance strategy to capture image segments serving as inputs to a model that predicts travel costs. We ablate the problem with a number of training modalities and demonstrate that the differentiable optimisation approach outperforms random search strategies.

OPO: Making Decision-Focused Data Acquisition Decisions

TL;DR

This work proposes a model for making data acquisition decisions for variables in contextual stochastic optimisation problems in which the acquisition of contextual variables is costly and consequently constrained and demonstrates that the differentiable optimisation approach outperforms random search strategies.

Abstract

We propose a model for making data acquisition decisions for variables in contextual stochastic optimisation problems. Data acquisition decisions are typically treated as separate and fixed. We explore problem settings in which the acquisition of contextual variables is costly and consequently constrained. The data acquisition problem is often solved heuristically for proxy objectives such as coverage. The more intuitive objective is the downstream decision quality as a result of data acquisition decisions. The whole pipeline can be characterised as an optimise-then-predict-then-optimise (OPO) problem. Analogously, much recent research has focused on how to integrate prediction and optimisation (PO) in the form of decision-focused learning. We propose leveraging differentiable optimisation to extend the integration to data acquisition. We solve the data acquisition problem with well-defined constraints by learning a surrogate linear objective function. We demonstrate an application of this model on a shortest path problem for which we first have to set a drone reconnaissance strategy to capture image segments serving as inputs to a model that predicts travel costs. We ablate the problem with a number of training modalities and demonstrate that the differentiable optimisation approach outperforms random search strategies.

Paper Structure

This paper contains 29 sections, 10 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Optimise-Predict-Optimise Problems
  3. Modelling DA
  4. Contrast with Feature Selection
  5. Prediction
  6. Contextual Decision Task
  7. DFL or PFL
  8. PFL Loss
  9. DFL Loss
  10. Optimising the Surrogate
  11. Differentiation
  12. Counterfactual Gradient
  13. Differentiable Optimisation
  14. Optimisation Strategies
  15. Random search over pretrained
  16. ...and 14 more sections

Figures (2)

  • Figure 1: OPO stages for a single instance on the Drone Reconnaissance For Shortest Path experiment from a configuration with warm-starting, learnt $\bm{\pi}$, fine-tuning, and DFL loss. Blue to yellow in \ref{['fig:1']} and \ref{['fig:4']} corresponds to low to high. Results for \ref{['fig:2']}, \ref{['fig:5']}, and \ref{['fig:6']} are binary: yellow corresponds to $1$ and purple to $0$.
  • Figure 2: Distribution of mean validation set results for the random search strategy. We note the best performing initialisation. We do not list results of DFL trained on PFL as they are obviously not competitive.