Alfredo Torrico

Omar El Housni, Ulysse Hennebelle, Alfredo Torrico

To address efficiency and design challenges in choice-based matching platforms, we introduce a two-sided assortment optimization framework under general choice preferences. The goal in this problem is to maximize the expected number of matches by deciding which assortments are displayed to the agents and the order in which they are shown. In this context, we identify several classes of policies that platforms can use in their design. Our goals are: (1) to measure the value that one class of policies has over another one, and (2) to approximately solve the optimization problem itself for a given class. For (1), we define the adaptivity gap as the worst-case ratio between the optimal values of two different policy classes. First, we show that the gap between the class of policies that statically show assortments to one-side first and the class of policies that adaptively show assortments to one-side first is exactly $e/(e-1)$. Second, we show that the gap between the latter class of policies and the fully adaptive class of policies that show assortments to agents one by one is exactly $2$. We also note that the worst policies are those who simultaneously show assortments to all the agents. For (2), we first design a polynomial time algorithm that achieves a $1/4$ approximation factor within the class of policies that adaptively show assortments to agents one by one. Furthermore, when agents' preferences are governed by multinomial-logit models, we show that a 0.067 approximation factor can be obtained within the class of policies that show assortments to all agents at once. We further generalize our results to constrained assortment settings, where we impose an upper bound on the size of the displayed assortments. Finally, we present a computational study to evaluate the empirical performance of our theoretical guarantees.

Alfredo Torrico, Natthawut Boonsiriphatthanajaroen, Nikhil Garg et al.

Congestion pricing is used to raise revenues and reduce traffic and pollution. However, people have heterogeneous spatial demand patterns and willingness (or ability) to pay tolls, and so pricing may have substantial equity implications. We develop a data-driven approach to design congestion pricing given policymakers' equity and efficiency objectives. First, algorithmically, we extend the Markovian traffic equilibrium setting introduced by Baillon & Cominetti (2008) to model heterogeneous populations and incorporate prices and outside options such as public transit. In this setting, we show that a unique equilibrium exists. Second, via a detailed case study, we empirically evaluate various pricing schemes using data collected by an industry partner in the city of Bogota, one of the most congested cities in the world. We find that pricing personalized to each economic stratum can be substantially more efficient and equitable than uniform pricing; however, non-personalized but area-based pricing can recover much of the gap.

Sebastian Pokutta, Mohit Singh, Alfredo Torrico

In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This algorithm theoretically performs less function calls than previous works at cost of adding more elements to the final solution. We also provide significant implementation improvements showing that our algorithm outperforms the algorithms in the existing literature. We finally assess the performance of our contributions in three real-world applications.