Robust Data-driven Prescriptiveness Optimization
Authors: Mehran Poursoltani, Erick Delage, Angelos Georghiou
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we present a numerical study that compares the performance of DRPCR against three other data-driven benchmark methods to evaluate its robustness to perturbations of the data generating process. Specifically, we will observe how these models react to the situation where one faces a distribution shift for . In a vehicle routing problem with travel time uncertainties, this can be interpreted as a shift in the distribution of the travel times, for instance, when a special event is happening in the town. Alternatively, one can think of an inventory management problem where the manager faces a shift in the demand distribution, e.g., an unforeseen increase in demand for sanitizer during the first days of an epidemic. |
| Researcher Affiliation | Academia | Mehran Poursoltani 1 Erick Delage 2 Angelos Georghiou 3 1Desautels Faculty of Management, Mc Gill University, Montr eal, Canada 2GERAD & Department of Decision Sciences, HEC Montr eal, Montr eal, Canada 3Department of Business and Public Administration, University of Cyprus, Nicosia, Cyprus. |
| Pseudocode | Yes | Algorithm 1 Bisection algorithm for DRPCR Algorithm 2 Algorithm for calibrating the size of the ambiguity set (α) for DRPCR Algorithm 3 Algorithm for calibrating the size of the ambiguity set (α) for CVa R-loss/CVa R-regret Algorithm 4 Algorithm for generating random symmetric positive-definite matrix Algorithm 5 Algorithm for generating random covariance matrix with arbitrary standard deviations |
| Open Source Code | Yes | The code used for the numerical experiments is available at https://github.com/erickdelage/robust_prescriptive_opt. |
| Open Datasets | No | The application that we consider for our numerical experiments is a shortest path problem described in Kallus & Mao 2023. A directed graph is defined as G = (V, A), where V denotes the set of nodes and A V V is the set of arcs, i.e., ordered pairs (i, j) of nodes describing the existence of a directed path from node i to node j. The corresponding travel time of such an arc is assumed to be (i,j). The objective of this problem is to identify the shortest path from an origin (node o) to a destination (node d). Moving away from an ideal world of known parameters gives rise to a stochastic version of this problem. In this setting, the traveling times along the arcs |A| are uncertain; however, one might still have access to side information or observed covariates. In this case, aiming at minimizing the expected travel time leads to the following CSO problem: x ( ) arg min x X E F | [x ], (15) x(i,j) {0, 1} (i, j) A P j:(o,j) A x(o,j) P j:(j,o) A x(j,o) = 1 P j:(d,j) A x(d,j) P j:(j,d) A x(j,d) = 1 P j:(i,j) A x(i,j) P j:(j,i) A x(j,i) = 0 i V \ {o, d} and x(i,j) = 1 if we decide to travel from node i to node j and x(i,j) = 0 otherwise. Unlike Kallus & Mao 2023, we enforce the integrality constraints. Furthermore, F | denotes the conditional distribution inferred from the training dataset. |
| Dataset Splits | Yes | Both the training and validation datasets consist of 400 data points, while the test set contains 1000 data points and is used to measure the out-of-sample performance. |
| Hardware Specification | Yes | All optimization problems are implemented in Python and solved using Gurobi 8.1.1 on a machine featuring an Intel processor Xeon(R) CPU E5-2687W v3 @ 3.10GHz 3.10 GHz (2 processors) and 128 GB RAM. |
| Software Dependencies | Yes | All optimization problems are implemented in Python and solved using Gurobi 8.1.1 |
| Experiment Setup | No | The paper describes the calibration procedure for alpha and gamma, but does not provide the specific hyperparameter values used in the final models or other typical machine learning hyperparameters (e.g., for random forests). |