arXiv subjects

Andrea Lodi

Publications and source records attributed to Andrea Lodi.

At least 91 records · Page 5Linked to original sources

arXiv2021

On the estimation of discrete choice models to capture irrational customer behaviors

The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as halo effects, that are incompatible with this framework. Models belonging to the Random Utility Maximization family may therefore not accurately capture such irrational behavior. Hence, more general choice models, overcoming such limitations, have been proposed. However, the flexibility of such models comes at the price of increased risk of overfitting. As such, estimating such models remains a challenge. In this work, we propose an estimation method for the recently proposed Generalized Stochastic Preference choice model, which subsumes the family of Random Utility Maximization models and is capable of capturing halo effects. Specifically, we show how to use partially-ranked preferences to efficiently model rational and irrational customer types from transaction data. Our estimation procedure is based on column generation, where relevant customer types are efficiently extracted by expanding a tree-like data structure containing the customer behaviors. Further, we propose a new dominance rule among customer types whose effect is to prioritize low orders of interactions among products. An extensive set of experiments assesses the predictive accuracy of the proposed approach. Our results show that accounting for irrational preferences can boost predictive accuracy by 12.5% on average, when tested on a real-world dataset from a large chain of grocery and drug stores.

econ.EM↗

arXiv2021

Assessing the Impact: Does an Improvement to a Revenue Management System Lead to an Improved Revenue?

Airlines and other industries have been making use of sophisticated Revenue Management Systems to maximize revenue for decades. While improving the different components of these systems has been the focus of numerous studies, estimating the impact of such improvements on the revenue has been overlooked in the literature despite its practical importance. Indeed, quantifying the benefit of a change in a system serves as support for investment decisions. This is a challenging problem as it corresponds to the difference between the generated value and the value that would have been generated keeping the system as before. The latter is not observable. Moreover, the expected impact can be small in relative value. In this paper, we cast the problem as counterfactual prediction of unobserved revenue. The impact on revenue is then the difference between the observed and the estimated revenue. The originality of this work lies in the innovative application of econometric methods proposed for macroeconomic applications to a new problem setting. Broadly applicable, the approach benefits from only requiring revenue data observed for origin-destination pairs in the network of the airline at each day, before and after a change in the system is applied. We report results using real large-scale data from Air Canada. We compare a deep neural network counterfactual predictions model with econometric models. They achieve respectively 1% and 1.1% of error on the counterfactual revenue predictions, and allow to accurately estimate small impacts (in the order of 2%).

cs.LG↗

arXiv2021

Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies

Branch and Bound (B&B) is the exact tree search method typically used to solve Mixed-Integer Linear Programming problems (MILPs). Learning branching policies for MILP has become an active research area, with most works proposing to imitate the strong branching rule and specialize it to distinct classes of problems. We aim instead at learning a policy that generalizes across heterogeneous MILPs: our main hypothesis is that parameterizing the state of the B&B search tree can aid this type of generalization. We propose a novel imitation learning framework, and introduce new input features and architectures to represent branching. Experiments on MILP benchmark instances clearly show the advantages of incorporating an explicit parameterization of the state of the search tree to modulate the branching decisions, in terms of both higher accuracy and smaller B&B trees. The resulting policies significantly outperform the current state-of-the-art method for "learning to branch" by effectively allowing generalization to generic unseen instances.

cs.LG↗

arXiv2021

Ecole: A Library for Learning Inside MILP Solvers

In this paper we describe Ecole (Extensible Combinatorial Optimization Learning Environments), a library to facilitate integration of machine learning in combinatorial optimization solvers. It exposes sequential decision making that must be performed in the process of solving as Markov decision processes. This means that, rather than trying to predict solutions to combinatorial optimization problems directly, Ecole allows machine learning to work in cooperation with a state-of-the-art a mixed-integer linear programming solver that acts as a controllable algorithm. Ecole provides a collection of computationally efficient, ready to use learning environments, which are also easy to extend to define novel training tasks. Documentation and code can be found at https://www.ecole.ai.

cs.LG↗

arXiv2021

Learning to Schedule Heuristics in Branch-and-Bound

Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances.

cs.LG↗

arXiv2021

Heuristics for optimizing 3D mapping missions over swarm-powered ad hoc clouds

Drones have been getting more and more popular in many economy sectors. Both scientific and industrial communities aim at making the impact of drones even more disruptive by empowering collaborative autonomous behaviors -- also known as swarming behaviors -- within fleets of multiple drones. In swarming-powered 3D mapping missions, unmanned aerial vehicles typically collect the aerial pictures of the target area whereas the 3D reconstruction process is performed in a centralized manner. However, such approaches do not leverage computational and storage resources from the swarm members.We address the optimization of a swarm-powered distributed 3D mapping mission for a real-life humanitarian emergency response application through the exploitation of a swarm-powered ad hoc cloud. Producing the relevant 3D maps in a timely manner, even when the cloud connectivity is not available, is crucial to increase the chances of success of the operation. In this work, we present a mathematical programming heuristic based on decomposition and a variable neighborhood search heuristic to minimize the completion time of the 3D reconstruction process necessary in such missions. Our computational results reveal that the proposed heuristics either quickly reach optimality or improve the best known solutions for almost all tested realistic instances comprising up to 1000 images and fifteen drones.

eess.SP↗

arXiv2021

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second stage problem, conditionally on the first stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training dataset consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

cs.LG↗

arXiv2021

The Covering-Assignment Problem for Swarm-powered Ad-hoc Clouds: A Distributed 3D Mapping Use-case

The popularity of drones is rapidly increasing across the different sectors of the economy. Aerial capabilities and relatively low costs make drones the perfect solution to improve the efficiency of those operations that are typically carried out by humans (e.g., building inspection, photo collection). The potential of drone applications can be pushed even further when they are operated in fleets and in a fully autonomous manner, acting de facto as a drone swarm. Besides automating field operations, a drone swarm can serve as an ad-hoc cloud infrastructure built on top of computing and storage resources available across the swarm members and other connected elements. Even in the absence of Internet connectivity, this cloud can serve the workloads generated by the swarm members themselves, as well as by the field agents operating within the area of interest. By considering the practical example of a swarm-powered 3D reconstruction application, we present a new optimization problem for the efficient generation and execution, on top of swarm-powered ad-hoc cloud infrastructure, of multi-node computing workloads subject to data geolocation and clustering constraints. The objective is the minimization of the overall computing times, including both networking delays caused by the inter-drone data transmission and computation delays. We prove that the problem is NP-hard and present two combinatorial formulations to model it. Computational results on the solution of the formulations show that one of them can be used to solve, within the configured time-limit, more than 50% of the considered real-world instances involving up to two hundred images and six drones.

eess.SP↗

arXiv2021

Predicting the probability distribution of bus travel time to move towards reliable planning of public transport services

An important aspect of the quality of a public transport service is its reliability, which is defined as the invariability of the service attributes. Preventive measures taken during planning can reduce risks of unreliability throughout operations. In order to tackle reliability during the service planning phase, a key piece of information is the long-term prediction of the density of the travel time, which conveys the uncertainty of travel times. We introduce a reliable approach to one of the problems of service planning in public transport, namely the Multiple Depot Vehicle Scheduling Problem (MDVSP), which takes as input a set of trips and the probability density function (p.d.f.) of the travel time of each trip in order to output delay-tolerant vehicle schedules. This work empirically compares probabilistic models for the prediction of the conditional p.d.f. of the travel time, as a first step towards reliable MDVSP solutions. Two types of probabilistic models, namely similarity-based density estimation models and a smoothed Logistic Regression for probabilistic classification model, are compared on a dataset of more than 41,000 trips and 50 bus routes of the city of Montréal. The result of a vast majority of probabilistic models outperforms that of a Random Forests model, which is not inherently probabilistic, thus highlighting the added value of modeling the conditional p.d.f. of the travel time with probabilistic models. A similarity-based density estimation model using a $k$ Nearest Neighbors method and a Kernel Density Estimation predicted the best estimate of the true conditional p.d.f. on this dataset.

cs.LG↗

arXiv2020

Computing Nash equilibria for integer programming games

The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set of linear constraints together with integer requirements. Many real-world problems can suitably be fit in this class, and hence anticipating IPG outcomes is of crucial value for policy makers and regulators. Nash equilibria have been widely accepted as the solution concept of a game. Consequently, their computation provides a reasonable prediction of the games outcome. In this paper, we start by showing the computational complexity of deciding the existence of a Nash equilibrium for an IPG. Then, using sufficient conditions for their existence, we develop two general algorithmic approaches that are guaranteed to approximate an equilibrium under mild conditions. We also showcase how our methodology can be changed to determine other equilibria definitions. The performance of our methods is analyzed through computational experiments in a knapsack game, a competitive lot-sizing game, and a kidney exchange game. To the best of our knowledge, this is the first time that equilibria computation methods for general integer programming games have been designed and computationally tested.

cs.GT↗

arXiv2020

Stochastic Damped L-BFGS with Controlled Norm of the Hessian Approximation

We propose a new stochastic variance-reduced damped L-BFGS algorithm, where we leverage estimates of bounds on the largest and smallest eigenvalues of the Hessian approximation to balance its quality and conditioning. Our algorithm, VARCHEN, draws from previous work that proposed a novel stochastic damped L-BFGS algorithm called SdLBFGS. We establish almost sure convergence to a stationary point and a complexity bound. We empirically demonstrate that VARCHEN is more robust than SdLBFGS-VR and SVRG on a modified DavidNet problem -- a highly nonconvex and ill-conditioned problem that arises in the context of deep learning, and their performance is comparable on a logistic regression problem and a nonconvex support-vector machine problem.

cs.LG↗

arXiv2020

Game theoretical analysis of Kidney Exchange Programs

The goal of a kidney exchange program (KEP) is to maximize number of transplants within a pool of incompatible patient-donor pairs by exchanging donors. A KEP can be modelled as a maximum matching problem in a graph. A KEP between incompatible patient-donor from pools of several hospitals, regions or countries has the potential to increase the number of transplants. These entities aim is to maximize the transplant benefit for their patients, which can lead to strategic behaviours. Recently, this was formulated as a non-cooperative two-player game and the game solutions (equilibria) were characterized when the entities objective function is the number of their patients receiving a kidney. In this paper, we generalize these results for $N$-players and discuss the impact in the game solutions when transplant information quality is introduced. Furthermore, the game theory model is analyzed through computational experiments on instances generated through the Canada Kidney Paired Donation Program. These experiments highlighting the importance of using the concept of Nash equilibrium, as well as, the anticipation of the necessity to further research for supporting police makers once measures on transplant quality are available.

cs.GT↗

arXiv2020

Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers

We present Ecole, a new library to simplify machine learning research for combinatorial optimization. Ecole exposes several key decision tasks arising in general-purpose combinatorial optimization solvers as control problems over Markov decision processes. Its interface mimics the popular OpenAI Gym library and is both extensible and intuitive to use. We aim at making this library a standardized platform that will lower the bar of entry and accelerate innovation in the field. Documentation and code can be found at https://www.ecole.ai.

cs.LG↗

arXiv2020

Hybrid Models for Learning to Branch

A recent Graph Neural Network (GNN) approach for learning to branch has been shown to successfully reduce the running time of branch-and-bound algorithms for Mixed Integer Linear Programming (MILP). While the GNN relies on a GPU for inference, MILP solvers are purely CPU-based. This severely limits its application as many practitioners may not have access to high-end GPUs. In this work, we ask two key questions. First, in a more realistic setting where only a CPU is available, is the GNN model still competitive? Second, can we devise an alternate computationally inexpensive model that retains the predictive power of the GNN architecture? We answer the first question in the negative, and address the second question by proposing a new hybrid architecture for efficient branching on CPU machines. The proposed architecture combines the expressive power of GNNs with computationally inexpensive multi-layer perceptrons (MLP) for branching. We evaluate our methods on four classes of MILP problems, and show that they lead to up to 26% reduction in solver running time compared to state-of-the-art methods without a GPU, while extrapolating to harder problems than it was trained on. The code for this project is publicly available at https://github.com/pg2455/Hybrid-learn2branch.

cs.LG↗

arXiv2020

Disjunctive cuts in Mixed-Integer Conic Optimization

This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization condition on its resolution. In particular, we show that a careful selection of normalization guarantees its solvability and conic strong duality. Then, we highlight the shortcomings of separating conic-infeasible points in an outer-approximation context, and propose conic extensions to the classical lifting and monoidal strengthening procedures. Finally, we assess the computational behavior of various normalization conditions in terms of gap closed, computing time and cut sparsity. In the process, we show that our approach is competitive with the internal lift-and-project cuts of a state-of-the-art solver.

math.OC↗

arXiv2020

Change Point Detection by Cross-Entropy Maximization

Many offline unsupervised change point detection algorithms rely on minimizing a penalized sum of segment-wise costs. We extend this framework by proposing to minimize a sum of discrepancies between segments. In particular, we propose to select the change points so as to maximize the cross-entropy between successive segments, balanced by a penalty for introducing new change points. We propose a dynamic programming algorithm to solve this problem and analyze its complexity. Experiments on two challenging datasets demonstrate the advantages of our method compared to three state-of-the-art approaches.

cs.LG↗

arXiv2020

Reinforcement Learning Based Penetration Testing of a Microgrid Control Algorithm

Microgrids (MGs) are small-scale power systems which interconnect distributed energy resources and loads within clearly defined regions. However, the digital infrastructure used in an MG to relay sensory information and perform control commands can potentially be compromised due to a cyberattack from a capable adversary. An MG operator is interested in knowing the inherent vulnerabilities in their system and should regularly perform Penetration Testing (PT) activities to prepare for such an event. PT generally involves looking for defensive coverage blindspots in software and hardware infrastructure, however the logic in control algorithms which act upon sensory information should also be considered in PT activities. This paper demonstrates a case study of PT for an MG control algorithm by using Reinforcement Learning (RL) to uncover malicious input which compromises the effectiveness of the controller. Through trial-and-error episodic interactions with a simulated MG, we train an RL agent to find malicious input which reduces the effectiveness of the MG controller.

eess.SY↗

arXiv2020

Design and implementation of a modular interior-point solver for linear optimization

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous interior-point algorithm with multiple centrality corrections, and therefore handles unbounded and infeasible problems. The solver is written in Julia, thus allowing for a flexible and efficient implementation: Tulip's algorithmic framework is fully disentangled from linear algebra implementations and from a model's arithmetic. In particular, this allows to seamlessly integrate specialized routines for structured problems. Extensive computational results are reported. We find that Tulip is competitive with open-source interior-point solvers on the H. Mittelmann's benchmark of barrier linear programming solvers. Furthermore, we design specialized linear algebra routines for structured master problems in the context of Dantzig-Wolfe decomposition. These routines yield a tenfold speedup on large and dense instances that arise in power systems operation and two-stage stochastic programming, thereby outperforming state-of-the-art commercial interior point method solvers. Finally, we illustrate Tulip's ability to use different levels of arithmetic precision by solving problems in extended precision.

math.OC↗