Margarida Carvalho

Working paper, November 2026.
Despite their widespread success across machine learning, the learning dynamics and generalization properties of neural networks remain poorly understood. The neural tangent kernel (NTK) provides an analytical characterization of the learning dynamics of infinitely wide neural networks and serves as a useful proxy for finite-width networks in supervised learning. In this work, we extend the NTK framework to reinforcement learning (RL) by introducing a temporal-difference (TD) flow formulation that accommodates time-varying mini-batches and TD targets, yielding a closed-form solution for value function evolution in an overparametrized setting. We also devise an optimization-based state-space exploration method that leverages the closed-form solution, coupled with constraints on the environment, to model the set of feasible states. On a deterministic grid environment, we validate that the proposed RL-based NTK formulation is indeed learning efficiently and adapting to the distribution shift in the training data distribution, and we demonstrate that the resulting exploration strategy improves sample efficiency. To our knowledge, this is the first work to extend NTK theory to characterize the learning dynamics of RL training with time-varying mini-batches and TD updates.
Working paper, October 2026.
General-sum games are more challenging than fully cooperative or adversarial settings because agents may deceive or exploit one another. Achieving high social welfare requires sustained cooperation, while a single defection can drive agents toward a welfare suboptimal Nash equilibrium. Moreover, assuming access to other agents' rewards or internal states is often unrealistic and implicitly introduces additional cooperation into the setting. To address this issue, we introduce Reciprocal Q-Augmentation (RQA), a method that uses a latent-variable opponent model to augment the Q-function with estimates of how one's actions affects other agents. RQA allows agents to learn both cooperative and defective policies using only their own Q-function. We show that, in social dilemmas, agents that all follow the cooperative policy of RQA learn to cooperate faster and reach higher levels of cooperation than fully cooperative algorithms. Moreover, a single RQA agent that switches appropriately between its cooperative and defecting policies can induce cooperation in agents trained with standard RL algorithms, which would otherwise end up defecting. We evaluate our approach on the Iterated Prisoner's Dilemma, Iterated Traveler's Dilemma, Iterated Stag Hunt, and CleanUp-Lite. Our experiments show that the algorithms implementing RQA outperforms fully cooperative methods with shared rewards and enables cooperation with algorithms that otherwise fail to reach high social welfare.
Journal of the Operational Research Society, Accepted paper, October 2026. (ArXiv version)
T. M. Nguyen was a finalist of the 2026 CORS Queueing and Applied Probability SIG Student Paper Competition for this work.
Electric vehicle (EV) public charging infrastructure planning faces significant challenges in competitive markets, where multiple service providers affect congestion and user behavior. This work extends existing modeling frameworks by incorporating the presence of competitors' stations and more realistic queueing systems. First, we analyze three finite queueing systems, M/M/1/K, M/M/s/K, and M/Er/s/K, with varying numbers of servers (charging outlets) and service time distributions, deriving analytic expressions for user behavior metrics. Second, we embed the queueing-based user behavior model into a bilevel program, where the upper level locates new charging stations to maximize accessibility (throughput), and the lower level captures users' station choices via a user equilibrium. Third, we apply a reformulation from competitive congested user-choice facility location models to approximately solve the bilevel problem and introduce a surrogate-based heuristic to enhance scalability. Fourth, we showcase our methodology on a real-world case study of an urban area in Montreal (Canada), offering managerial insights into how user-choice behavior assumptions and competition affect throughput and location decisions. The results demonstrate that our model yields (re)location strategies that outperform the existing network. More broadly, this approach provides a tool for incorporating charging service quality-through queueing metrics-and existing competition into station planning.
Mathematics of Operations Research, Accepted, August 2026. (ArXiv version)
Motivated by the challenges faced by choice-based matching platforms, in this work, we study a generalization of the two-sided assortment optimization model. Specifically, this model consists of two sides (e.g., customers and suppliers) who have preferences over the opposite side in the form of discrete choice models. A matching is realized through a two-step process where the platform’s decision is to initially present to each agent on one side an assortment of users of the opposite side. The ultimate goal of the platform is to maximize the total expected revenue collected from the matching. Because of the computational complexity of this problem, we focus on the design of approximation algorithms with constant-factor guarantees for the constrained version of the problem under general choice preferences. First, to the best of our knowledge, we are the first to draw connections with the literature of submodular optimization and show that one-sided choice-oblivious approaches perform arbitrarily badly. Second, we show that, for the general setting, there exists a two-sided choice-aware randomized algorithm that achieves a (1−1/e)-approximation factor, which is the best possible. Third, we design an algorithm that is asymptotically optimal when one side follows the well-known multinomial logit (MNL) choice model under the small probability regime. Fourth, we pro