arXiv subjects

Maria Bazotte

Publications and source records attributed to Maria Bazotte.

3 recordsLinked to original sources

arXiv2026

Intermediate Bilevel Optimization: Modeling Endogenous Follower Tie-Breaking Behavior

In bilevel optimization, optimistic and pessimistic follower behaviors are the most commonly used forms to define how the follower ties-breaks among multiple optimal solutions. In this work, we go beyond these extreme tie-breaking behaviors and investigate the intermediate bilevel optimization program (I-BO), where the follower's selected optimal response is a decision-dependent random event, with a probability measure influenced by the leader's decision. We formally introduce a class of such endogenous measures, including the special case of strong-weak decision-dependent I-BO. We reformulate the I-BO as a Transformed I-BO (T-I-BO) with exogenous uncertainty by defining inverse and Markov-chain transformations, which represent the follower's response as a function of the leader's decision and exogenous randomness. We handle the T-I-BO's uncertainty via sample-average approximation (SAA), and we propose tailored approaches for its SAA program according to the chosen transformation. Computationally, our methods solve reasonable-sized instances efficiently and outperform the deterministic equivalent when available. Furthermore, experiments stress the critical need to accurately model follower tie-breaking behavior, particularly depending on its alignment with the leader's objective, as misspecification leads to suboptimal leader decisions.

math.OC↗

arXiv2025

Two-Stage Stochastic Capacity Expansion in Stable Matching under Truthful or Strategic Preference Uncertainty

Recent studies on many-to-one matching markets have explored agents with flexible capacity and truthful preference reporting, focusing on mechanisms that jointly design capacities and select a matching. However, in real-world applications such as school choice and residency matching, preferences are revealed after capacity decisions are made, with matching occurring afterward; uncertainty about agents' preferences must be considered during capacity planning. Moreover, even under strategy-proof mechanisms, agents may strategically misreport preferences based on beliefs about admission chances. We introduce a two-stage stochastic matching problem with uncertain preferences, using school choice as a case study. In the first stage, the clearinghouse expands schools' capacities before observing students' reported preferences. Students either report their true preferences, producing exogenous uncertainty, or act strategically, submitting reported preferences based on their true preferences and admission chances (which depend on capacities), introducing endogenous uncertainty. In the second stage, the clearinghouse computes the student-optimal stable matching based on schools' priorities and students' reported preferences. In strategic cases, endogenous reported preferences are utility-maximizing transformations of capacity decisions and exogenous true preferences; we handle uncertainty using sample average approximation(SAA). We develop behavior-based mathematical formulations and, due to problem complexity, propose Lagrangian- and local-search-based behavior-specific heuristics for near-optimal solutions. Our SAA-based approaches outperform the average scenario approach on students' matching preferences and admission outcomes, emphasizing the impact of stochastic preferences on capacity decisions. Student behavior notably influences capacity design, stressing the need to consider misreports.

cs.GT↗

arXiv2024

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↗