arXiv subjects

Thibaut Vidal

Publications and source records attributed to Thibaut Vidal.

At least 37 records · Page 2Linked to original sources

arXiv2025

Solving Two-Stage Stochastic Programs with Endogenous Uncertainty via Random Variable Transformation

Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model decisions. Few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We propose a general method for solving a class of these programs based on random variable transformation, a technique widely employed in probability and statistics. The random variable transformation converts a stochastic program with endogenous uncertainty (original program) into an equivalent stochastic program with decision-independent uncertainty (transformed program), for which solution procedures are well-studied. Additionally, endogenous uncertainty usually leads to nonlinear nonconvex programs, which are theoretically intractable. Nonetheless, we show that, for some classical endogenous distributions, the proposed method yields mixed-integer linear or convex programs with exogenous uncertainty. We validate this method by applying it to a network design and facility-protection problem, considering distinct decision-dependent distributions for the random variables. While the original formulation of this problem is nonlinear nonconvex for most endogenous distributions, the proposed method transforms it into mixed-integer linear programs with exogenous uncertainty. We solve these transformed programs with the sample average approximation method. We highlight the superior performance of our approach compared to solving the original program in the case a mixed-integer linear formulation of this program exists.

math.OC↗

arXiv2025

Free Lunch in the Forest: Functionally-Identical Pruning of Boosted Tree Ensembles

Tree ensembles, including boosting methods, are highly effective and widely used for tabular data. However, large ensembles lack interpretability and require longer inference times. We introduce a method to prune a tree ensemble into a reduced version that is "functionally identical" to the original model. In other words, our method guarantees that the prediction function stays unchanged for any possible input. As a consequence, this pruning algorithm is lossless for any aggregated metric. We formalize the problem of functionally identical pruning on ensembles, introduce an exact optimization model, and provide a fast yet highly effective method to prune large ensembles. Our algorithm iteratively prunes considering a finite set of points, which is incrementally augmented using an adversarial model. In multiple computational experiments, we show that our approach is a "free lunch", significantly reducing the ensemble size without altering the model's behavior. Thus, we can preserve state-of-the-art performance at a fraction of the original model's size.

cs.LG↗

arXiv2024

DistrictNet: Decision-aware learning for geographical districting

Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts. In logistics, it is a major strategic decision determining operating costs for several years. Solving districting problems using traditional methods is intractable even for small geographical areas and existing heuristics often provide sub-optimal results. We present a structured learning approach to find high-quality solutions to real-world districting problems in a few minutes. It is based on integrating a combinatorial optimization layer, the capacitated minimum spanning tree problem, into a graph neural network architecture. To train this pipeline in a decision-aware fashion, we show how to construct target solutions embedded in a suitable space and learn from target solutions. Experiments show that our approach outperforms existing methods as it can significantly reduce costs on real-world cities.

cs.LG↗

arXiv2024

Adaptive Partitioning for Chance-Constrained Problems with Finite Support

This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem is constructed to yield a bound on the optimal value of the original problem. We show how to adapt the partitioning of the scenario set so that our adaptive method returns the optimal solution of the original chance-constrained problem in a finite number of iterations. At the heart of the method lie two fundamental operations: refinement and merging. A refinement operation divides a subset of the partition, whereas a merging operation combines a group of subsets into one. We describe how to use these operations to enhance the bound obtained in each step of the method while preserving the small size of the reduced model. Under mild conditions, we prove that, for specific refinement and merge operations, the bound obtained after solving each reduced model strictly improves throughout the iterative process. Our general method allows the seamless integration of various computational enhancements, significantly reducing the computational time required to solve the reduced chance-constrained problems. The method's efficiency is assessed through numerical experiments on chance-constrained multidimensional knapsack problems. We study the impact of our method's components and compare its performance against other methods from the recent literature.

math.OC↗

arXiv2024

Trained Random Forests Completely Reveal your Dataset

We introduce an optimization-based reconstruction attack capable of completely or near-completely reconstructing a dataset utilized for training a random forest. Notably, our approach relies solely on information readily available in commonly used libraries such as scikit-learn. To achieve this, we formulate the reconstruction problem as a combinatorial problem under a maximum likelihood objective. We demonstrate that this problem is NP-hard, though solvable at scale using constraint programming -- an approach rooted in constraint propagation and solution-domain reduction. Through an extensive computational investigation, we demonstrate that random forests trained without bootstrap aggregation but with feature randomization are susceptible to a complete reconstruction. This holds true even with a small number of trees. Even with bootstrap aggregation, the majority of the data can also be reconstructed. These findings underscore a critical vulnerability inherent in widely adopted ensemble methods, warranting attention and mitigation. Although the potential for such reconstruction attacks has been discussed in privacy research, our study provides clear empirical evidence of their practicability.

cs.LG↗

arXiv2024

CF-OPT: Counterfactual Explanations for Structured Prediction

Optimization layers in deep neural networks have enjoyed a growing popularity in structured learning, improving the state of the art on a variety of applications. Yet, these pipelines lack interpretability since they are made of two opaque layers: a highly non-linear prediction model, such as a deep neural network, and an optimization layer, which is typically a complex black-box solver. Our goal is to improve the transparency of such methods by providing counterfactual explanations. We build upon variational autoencoders a principled way of obtaining counterfactuals: working in the latent space leads to a natural notion of plausibility of explanations. We finally introduce a variant of the classic loss for VAE training that improves their performance in our specific structured context. These provide the foundations of CF-OPT, a first-order optimization algorithm that can find counterfactual explanations for a broad class of structured learning architectures. Our numerical results show that both close and plausible explanations can be obtained for problems from the recent literature.

cs.LG↗

arXiv2024

Dual Policy Reinforcement Learning for Real-time Rebalancing in Bike-sharing Systems

Bike-sharing systems play a crucial role in easing traffic congestion and promoting healthier lifestyles. However, ensuring their reliability and user acceptance requires effective strategies for rebalancing bikes. This study introduces a novel approach to address the real-time rebalancing problem with a fleet of vehicles. It employs a dual policy reinforcement learning algorithm that decouples inventory and routing decisions, enhancing realism and efficiency compared to previous methods where both decisions were made simultaneously. We first formulate the inventory and routing subproblems as a multi-agent Markov Decision Process within a continuous time framework. Subsequently, we propose a DQN-based dual policy framework to jointly estimate the value functions, minimizing the lost demand. To facilitate learning, a comprehensive simulator is applied to operate under a first-arrive-first-serve rule, which enables the computation of immediate rewards across diverse demand scenarios. We conduct extensive experiments on various datasets generated from historical real-world data, affected by both temporal and weather factors. Our proposed algorithm demonstrates significant performance improvements over previous baseline methods. It offers valuable practical insights for operators and further explores the incorporation of reinforcement learning into real-world dynamic programming problems, paving the way for more intelligent and robust urban mobility solutions.

cs.LG↗

arXiv2024

Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles

Counterfactual explanations describe how to modify a feature vector in order to flip the outcome of a trained classifier. Obtaining robust counterfactual explanations is essential to provide valid algorithmic recourse and meaningful explanations. We study the robustness of explanations of randomized ensembles, which are always subject to algorithmic uncertainty even when the training data is fixed. We formalize the generation of robust counterfactual explanations as a probabilistic problem and show the link between the robustness of ensemble models and the robustness of base learners. We develop a practical method with good empirical performance and support it with theoretical guarantees for ensembles of convex base learners. Our results show that existing methods give surprisingly low robustness: the validity of naive counterfactuals is below $50\%$ on most data sets and can fall to $20\%$ on problems with many features. In contrast, our method achieves high robustness with only a small increase in the distance from counterfactual explanations to their initial observations.

cs.LG↗

arXiv2024

Learning-based Online Optimization for Autonomous Mobility-on-Demand Fleet Control

Autonomous mobility-on-demand systems are a viable alternative to mitigate many transportation-related externalities in cities, such as rising vehicle volumes in urban areas and transportation-related pollution. However, the success of these systems heavily depends on efficient and effective fleet control strategies. In this context, we study online control algorithms for autonomous mobility-on-demand systems and develop a novel hybrid combinatorial optimization enriched machine learning pipeline which learns online dispatching and rebalancing policies from optimal full-information solutions. We test our hybrid pipeline on large-scale real-world scenarios with different vehicle fleet sizes and various request densities. We show that our approach outperforms state-of-the-art greedy, and model-predictive control approaches with respect to various KPIs, e.g., by up to 17.1% and on average by 6.3% in terms of realized profit.

math.OC↗

arXiv2024

Contextual Stochastic Vehicle Routing with Time Windows

We study the vehicle routing problem with time windows (VRPTW) and stochastic travel times, in which the decision-maker observes related contextual information, represented as feature variables, before making routing decisions. Despite the extensive literature on stochastic VRPs, the integration of feature variables has received limited attention in this context. We introduce the contextual stochastic VRPTW, which minimizes the total transportation cost and expected late arrival penalties conditioned on the observed features. Since the joint distribution of travel times and features is unknown, we present novel data-driven prescriptive models that use historical data to provide an approximate solution to the problem. We distinguish the prescriptive models between point-based approximation, sample average approximation, and penalty-based approximation, each taking a different perspective on dealing with stochastic travel times and features. We develop specialized branch-price-and-cut algorithms to solve these data-driven prescriptive models. In our computational experiments, we compare the out-of-sample cost performance of different methods on instances with up to one hundred customers. Our results show that, surprisingly, a feature-dependent sample average approximation outperforms existing and novel methods in most settings.

cs.LG↗

arXiv2024

Combinatorial Optimization and Machine Learning for Dynamic Inventory Routing

We introduce a combinatorial optimization-enriched machine learning pipeline and a novel learning paradigm to solve inventory routing problems with stochastic demand and dynamic inventory updates. After each inventory update, our approach reduces replenishment and routing decisions to an optimal solution of a capacitated prize-collecting traveling salesman problem for which well-established algorithms exist. Discovering good prize parametrizations is non-trivial; therefore, we have developed a machine learning approach. We evaluate the performance of our pipeline in settings with steady-state and more complex demand patterns. Compared to previous works, the policy generated by our algorithm leads to significant cost savings, achieves lower inference time, and can even leverage contextual information.

math.OC↗

arXiv2024

Regularization and Optimization in Model-Based Clustering

Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical Gaussians to data that vastly deviates from such a distribution. In comparison, general Gaussian Mixture Models (GMMs) can fit richer structures but require estimating a quadratic number of parameters per cluster to represent the covariance matrices. This poses two main issues: (i) the underlying optimization problems are challenging due to their larger number of local minima, and (ii) their solutions can overfit the data. In this work, we design search strategies that circumvent both issues. We develop more effective optimization algorithms for general GMMs, and we combine these algorithms with regularization strategies that avoid overfitting. Through extensive computational analyses, we observe that optimization or regularization in isolation does not substantially improve cluster recovery. However, combining these techniques permits a completely new level of performance previously unachieved by k-means algorithm variants, unraveling vastly different cluster structures. These results shed new light on the current status quo between GMM and k-means methods and suggest the more frequent use of general GMMs for data exploration. To facilitate such applications, we provide open-source code as well as Julia packages (UnsupervisedClustering.jl and RegularizedCovarianceMatrices.jl) implementing the proposed techniques.

cs.LG↗

arXiv2024

A Survey of Contextual Optimization Methods for Decision Making under Uncertainty

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming.

math.OC↗

arXiv2023

Solving a Continent-Scale Inventory Routing Problem at Renault

This paper is the fruit of a partnership with Renault. Their backward logistic requires solving a continent-scale multi-attribute inventory routing problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers spread across a continent, our instances are orders of magnitude larger than those in the literature. Existing algorithms do not scale. We propose a large neighborhood search (LNS). To make it work, (1) we generalize existing split delivery vehicle routing problem and IRP neighborhoods to this context, (2) we turn a state-of-the art matheuristic for medium-scale IRP into a large neighborhood, and (3) we introduce two novel perturbations: the reinsertion of a customer and that of a commodity into the IRP solution. We also derive a new lower bound based on a flow relaxation. In order to stimulate the research on large-scale IRP, we introduce a library of industrial instances. We benchmark our algorithms on these instances and make our code open-source. Extensive numerical experiments highlight the relevance of each component of our LNS.

math.OC↗

arXiv2023

Explainable Data-Driven Optimization: From Context to Decision and Back Again

Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the classification setting, explaining decision pipelines involving learning algorithms remains unaddressed. This lack of interpretability can block the adoption of data-driven solutions as practitioners may not understand or trust the recommended decisions. We bridge this gap by introducing a counterfactual explanation methodology tailored to explain solutions to data-driven problems. We introduce two classes of explanations and develop methods to find nearest explanations of random forest and nearest-neighbor predictors. We demonstrate our approach by explaining key problems in operations management such as inventory management and routing.

cs.LG↗

arXiv2023

An efficient bundle-based approach for the share-a-ride problem

Some of today's most significant challenges in urban environments concern individual mobility and rapid parcel delivery. With the surge of e-commerce and the ever-increasing volume of goods to be handled, new logistic solutions are in high demand. The share-a-ride problem (SARP) was proposed as one such solution, combining people and parcel transportation in taxis. This is an NP-hard problem and thus obtaining optimal solutions can be computationally costly. In this paper, we work with a variation of SARP for ride-hailing systems, which can be formulated as a multi-depot open generalised vehicle routing problem with time windows. We present and solve a mixed-integer linear programming (MILP) formulation for this problem that bundles requests together, and we compare its results to a previously proposed two-stage method. The latter solves the so-called freight insertion problem (FIP) in the second stage, for which we consider two versions, and the problem consists of inserting parcels into predefined passenger routes obtained in the first stage. We tested the methods in three sets of instances. The developed bundle-based approach outperformed both FIP versions in solution quality and in the service of parcels. Our method also compares favourably when it comes to reducing the amount of deadheading distance.

cs.DS↗

arXiv2023

Recent Advances in Vehicle Routing with Stochastic Demands: Bayesian Learning for Correlated Demands and Elementary Branch-Price-and-Cut

We consider the vehicle routing problem with stochastic demands (VRPSD), a stochastic variant of the well-known VRP in which demands are only revealed upon arrival of the vehicle at each customer. Motivated by the significant recent progress on VRPSD research, we begin this paper by summarizing the key new results and methods for solving the problem. In doing so, we discuss the main challenges associated with solving the VRPSD under the chance-constraint and the restocking-based perspectives. Once we cover the current state-of-the-art, we introduce two major methodological contributions. First, we present a branch-price-and-cut (BP&C) algorithm for the VRPSD under optimal restocking. The method, which is based on the pricing of elementary routes, compares favorably with previous algorithms and allows the solution of several open benchmark instances. Second, we develop a demand model for dealing with correlated customer demands. The central concept in this model is the "external factor", which represents unknown covariates that affect all demands. We present a Bayesian-based, iterated learning procedure to refine our knowledge about the external factor as customer demands are revealed. This updated knowledge is then used to prescribe optimal replenishment decisions under demand correlation. Computational results demonstrate the efficiency of the new BP&C method and show that cost savings above 10% may be achieved when restocking decisions take account of demand correlation. Lastly, we motivate a few research perspectives that, as we believe, should shape future research on the VRPSD.

math.OC↗

arXiv2023

Electric Vehicle Fleets: Scalable Route and Recharge Scheduling through Column Generation

The rise of battery-powered vehicles has led to many new technical and methodological hurdles. Among these, the efficient planning of an electric fleet to fulfill passenger transportation requests still represents a major challenge. This is due to the specific constraints of electric vehicles, bound by their battery autonomy and necessity of recharge planning, and the large scale of the operations, which challenges existing optimization algorithms. The purpose of this paper is to introduce a scalable column generation approach for routing and scheduling in this context. Our algorithm relies on four main ingredients: (i) a multigraph reformulation of the problem based on a characterization of non-dominated charging arcs, (ii) an efficient bi-directional pricing algorithm using tight backward bounds, (iii) sparsification approaches permitting to decrease the size of the subjacent graphs dramatically, and (iv) a diving heuristic, which locates near-optimal solutions in a fraction of the time needed for a complete branch-and-price. Through extensive computational experiments, we demonstrate that our approach significantly outperforms previous algorithms for this setting, leading to accurate solutions for problems counting several hundreds of requests.

math.OC↗