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.

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.

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.

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.

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.

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.

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.

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.

Regularization and Global 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 efficient global optimization algorithms for general GMMs, and we combine these algorithms with regularization strategies that avoid overfitting. Through extensive computational analyses, we observe that global 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.

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.