arXiv subjects

Arthur Delarue

Publications and source records attributed to Arthur Delarue.

9 recordsLinked to original sources

arXiv2025

Pricing Experiments in Matching Marketplaces under Interference: Designs and Estimators

Interference between treated and untreated units is a source of bias in marketplace experiments. In this paper, we specifically consider pricing interventions, in which a platform seeks to adjust base pricing levels at the marketplace level in order to increase demand. In a matching marketplace, this type of experiment leads to a crucial design question: should the platform match treated and untreated units differently because they paid different prices? We find that standard estimation techniques are biased, but the sign of this bias depends strongly on this design choice. Bias can be reduced by using the ``shadow price estimator'', which relies on the optimal dual solution of the platform's supply-demand matching problem -- especially when the platform chooses to ignore pricing differences at matching time. We validate our findings both theoretically in a fluid limit setting, and numerically in a finite-sample setting.

math.OC↗

arXiv2024

Adaptive Optimization for Prediction with Missing Data

When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with missing data as a two-stage adaptive optimization problem and propose a new class of models, adaptive linear regression models, where the regression coefficients adapt to the set of observed features. We show that some adaptive linear regression models are equivalent to learning an imputation rule and a downstream linear regression model simultaneously instead of sequentially. We leverage this joint-impute-then-regress interpretation to generalize our framework to non-linear models. In settings where data is strongly not missing at random, our methods achieve a 2-10% improvement in out-of-sample accuracy.

cs.LG↗

arXiv2023

Solving the Quadratic Assignment Problem using Deep Reinforcement Learning

The Quadratic Assignment Problem (QAP) is an NP-hard problem which has proven particularly challenging to solve: unlike other combinatorial problems like the traveling salesman problem (TSP), which can be solved to optimality for instances with hundreds or even thousands of locations using advanced integer programming techniques, no methods are known to exactly solve QAP instances of size greater than 30. Solving the QAP is nevertheless important because of its many critical applications, such as electronic wiring design and facility layout selection. We propose a method to solve the original Koopmans-Beckman formulation of the QAP using deep reinforcement learning. Our approach relies on a novel double pointer network, which alternates between selecting a location in which to place the next facility and a facility to place in the previous location. We train our model using A2C on a large dataset of synthetic instances, producing solutions with no instance-specific retraining necessary. Out of sample, our solutions are on average within 7.5% of a high-quality local search baseline, and even outperform it on 1.2% of instances.

cs.LG↗

arXiv2022

Reducing Marketplace Interference Bias Via Shadow Prices

Marketplace companies rely heavily on experimentation when making changes to the design or operation of their platforms. The workhorse of experimentation is the randomized controlled trial (RCT), or A/B test, in which users are randomly assigned to treatment or control groups. However, marketplace interference causes the Stable Unit Treatment Value Assumption (SUTVA) to be violated, leading to bias in the standard RCT metric. In this work, we propose techniques for platforms to run standard RCTs and still obtain meaningful estimates despite the presence of marketplace interference. We specifically consider a generalized matching setting, in which the platform explicitly matches supply with demand via a linear programming algorithm. Our first proposal is for the platform to estimate the value of global treatment and global control via optimization. We prove that this approach is unbiased in the fluid limit. Our second proposal is to compare the average shadow price of the treatment and control groups rather than the total value accrued by each group. We prove that this technique corresponds to the correct first-order approximation (in a Taylor series sense) of the value function of interest even in a finite-size system. We then use this result to prove that, under reasonable assumptions, our estimator is less biased than the RCT estimator. At the heart of our result is the idea that it is relatively easy to model interference in matching-driven marketplaces since, in such markets, the platform mediates the spillover.

math.OC↗

arXiv2021

Simple Imputation Rules for Prediction with Missing Data: Contrasting Theoretical Guarantees with Empirical Performance

Missing data is a common issue in real-world datasets. This paper studies the performance of impute-then-regress pipelines by contrasting theoretical and empirical evidence. We establish the asymptotic consistency of such pipelines for a broad family of imputation methods. While common sense suggests that a `good' imputation method produces datasets that are plausible, we show, on the contrary, that, as far as prediction is concerned, crude can be good. Among others, we find that mode-impute is asymptotically sub-optimal, while mean-impute is asymptotically optimal. We then exhaustively assess the validity of these theoretical conclusions on a large corpus of synthetic, semi-real, and real datasets. While the empirical evidence we collect mostly supports our theoretical findings, it also highlights gaps between theory and practice and opportunities for future research, regarding the relevance of the MAR assumption, the complex interdependency between the imputation and regression tasks, and the need for realistic synthetic data generation models.

stat.ML↗

arXiv2020

Reinforcement Learning with Combinatorial Actions: An Application to Vehicle Routing

Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for enumeration. We develop a framework for value-function-based deep reinforcement learning with a combinatorial action space, in which the action selection problem is explicitly formulated as a mixed-integer optimization problem. As a motivating example, we present an application of this framework to the capacitated vehicle routing problem (CVRP), a combinatorial optimization problem in which a set of locations must be covered by a single vehicle with limited capacity. On each instance, we model an action as the construction of a single route, and consider a deterministic policy which is improved through a simple policy iteration algorithm. Our approach is competitive with other reinforcement learning methods and achieves an average gap of 1.7% with state-of-the-art OR methods on standard library instances of medium size.

cs.LG↗

arXiv2020

From predictions to prescriptions: A data-driven response to COVID-19

The COVID-19 pandemic has created unprecedented challenges worldwide. Strained healthcare providers make difficult decisions on patient triage, treatment and care management on a daily basis. Policy makers have imposed social distancing measures to slow the disease, at a steep economic price. We design analytical tools to support these decisions and combat the pandemic. Specifically, we propose a comprehensive data-driven approach to understand the clinical characteristics of COVID-19, predict its mortality, forecast its evolution, and ultimately alleviate its impact. By leveraging cohort-level clinical data, patient-level hospital data, and census-level epidemiological data, we develop an integrated four-step approach, combining descriptive, predictive and prescriptive analytics. First, we aggregate hundreds of clinical studies into the most comprehensive database on COVID-19 to paint a new macroscopic picture of the disease. Second, we build personalized calculators to predict the risk of infection and mortality as a function of demographics, symptoms, comorbidities, and lab values. Third, we develop a novel epidemiological model to project the pandemic's spread and inform social distancing policies. Fourth, we propose an optimization model to re-allocate ventilators and alleviate shortages. Our results have been used at the clinical level by several hospitals to triage patients, guide care management, plan ICU capacity, and re-distribute ventilators. At the policy level, they are currently supporting safe back-to-work policies at a major institution and equitable vaccine distribution planning at a major pharmaceutical company, and have been integrated into the US Center for Disease Control's pandemic forecast.

stat.AP↗

arXiv2019

The Price of Interpretability

When quantitative models are used to support decision-making on complex and important topics, understanding a model's ``reasoning'' can increase trust in its predictions, expose hidden biases, or reduce vulnerability to adversarial attacks. However, the concept of interpretability remains loosely defined and application-specific. In this paper, we introduce a mathematical framework in which machine learning models are constructed in a sequence of interpretable steps. We show that for a variety of models, a natural choice of interpretable steps recovers standard interpretability proxies (e.g., sparsity in linear models). We then generalize these proxies to yield a parametrized family of consistent measures of model interpretability. This formal definition allows us to quantify the ``price'' of interpretability, i.e., the tradeoff with predictive accuracy. We demonstrate practical algorithms to apply our framework on real and synthetic datasets.

cs.LG↗

arXiv2019

Optimal Explanations of Linear Models

When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at interpreting models are often ad hoc and application-specific, and the concept of interpretability itself is not well-defined. We propose a general optimization framework to create explanations for linear models. Our methodology decomposes a linear model into a sequence of models of increasing complexity using coordinate updates on the coefficients. Computing this decomposition optimally is a difficult optimization problem for which we propose exact algorithms and scalable heuristics. By solving this problem, we can derive a parametrized family of interpretability metrics for linear models that generalizes typical proxies, and study the tradeoff between interpretability and predictive accuracy.

cs.LG↗