Migration as Submodular Optimization

Migration presents sweeping societal challenges that have recently attracted significant attention from the scientific community. One of the prominent approaches that have been suggested employs optimization and machine learning to match migrants to localities in a way that maximizes the expected number of migrants who find employment. However, it relies on a strong additivity assumption that, we argue, does not hold in practice, due to competition effects; we propose to enhance the data-driven approach by explicitly optimizing for these effects. Specifically, we cast our problem as the maximization of an approximately submodular function subject to matroid constraints, and prove that the worst-case guarantees given by the classic greedy algorithm extend to this setting. We then present three different models for competition effects, and show that they all give rise to submodular objectives. Finally, we demonstrate via simulations that our approach leads to significant gains across the board.Comment: Simulation code is available at https://github.com/pgoelz/migration

Combining Outcome-Based and Preference-Based Matching: A Constrained Priority Mechanism

We introduce a constrained priority mechanism that combines outcome-based matching from machine-learning with preference-based allocation schemes common in market design. Using real-world data, we illustrate how our mechanism could be applied to the assignment of refugee families to host country locations, and kindergarteners to schools. Our mechanism allows a planner to first specify a threshold $\bar g$ for the minimum acceptable average outcome score that should be achieved by the assignment. In the refugee matching context, this score corresponds to the predicted probability of employment, while in the student assignment context it corresponds to standardized test scores. The mechanism is a priority mechanism that considers both outcomes and preferences by assigning agents (refugee families, students) based on their preferences, but subject to meeting the planner's specified threshold. The mechanism is both strategy-proof and constrained efficient in that it always generates a matching that is not Pareto dominated by any other matching that respects the planner's threshold.Comment: This manuscript has been accepted for publication by Political Analysis and will appear in a revised form subject to peer review and/or input from the journal's editor. End-users of this manuscript may only make use of it for private research and study and may not distribute it furthe

Migrant Resettlement by Evolutionary Multi-objective Optimization

Migration has been a universal phenomenon, which brings opportunities as well as challenges for global development. As the number of migrants (e.g., refugees) increases rapidly in recent years, a key challenge faced by each country is the problem of migrant resettlement. This problem has attracted scientific research attention, from the perspective of maximizing the employment rate. Previous works mainly formulated migrant resettlement as an approximately submodular optimization problem subject to multiple matroid constraints and employed the greedy algorithm, whose performance, however, may be limited due to its greedy nature. In this paper, we propose a new framework MR-EMO based on Evolutionary Multi-objective Optimization, which reformulates Migrant Resettlement as a bi-objective optimization problem that maximizes the expected number of employed migrants and minimizes the number of dispatched migrants simultaneously, and employs a Multi-Objective Evolutionary Algorithm (MOEA) to solve the bi-objective problem. We implement MR-EMO using three MOEAs, the popular NSGA-II, MOEA/D as well as the theoretically grounded GSEMO. To further improve the performance of MR-EMO, we propose a specific MOEA, called GSEMO-SR, using matrix-swap mutation and repair mechanism, which has a better ability to search for feasible solutions. We prove that MR-EMO using either GSEMO or GSEMO-SR can achieve better theoretical guarantees than the previous greedy algorithm. Experimental results under the interview and coordination migration models clearly show the superiority of MR-EMO (with either NSGA-II, MOEA/D, GSEMO or GSEMO-SR) over previous algorithms, and that using GSEMO-SR leads to the best performance of MR-EMO

I Will Have Order! Optimizing Orders for Fair Reviewer Assignment

We present fast, fair, flexible, and welfare efficient algorithms for assigning reviewers to submitted conference papers. Our approaches extend picking sequence mechanisms, standard tools from the fair allocation literature to ensure approximate envy-freeness (typically envy-freeness up to one item, or EF1). However, fairness often comes at the cost of decreased efficiency. To overcome this challenge, we carefully select approximately optimal picking sequence orders. Applying a relaxation of submodularity, $\gamma$-weak submodularity, we show our Greedy Reviewer Round Robin (GRRR) approach is EF1 and yields a ${(1+\gamma)}$-approximation to the maximum welfare attainable by a round-robin picking sequence mechanism under any order. We present a weighted picking sequence mechanism called FairSequence that targets the Weighted EF1 criterion to offer fairness in a more general setting. Using data from three conferences, we show that FairSequence runs an order of magnitude faster and provides approximate envy-freeness guarantees that are violated by existing approaches. Its simple design also makes it very flexible to new assignment constraints. FairSequence is available in the OpenReview conference management platform, giving conference organizers access to faster reviewer assignment with high welfare and envy-freeness guarantees.Comment: 41 pages, 8 figures, extends initial version published at IJCAI 202

Diversity and Novelty: Measurement, Learning and Optimization

The primary objective of this dissertation is to investigate research methods to answer the question: ``How (and why) does one measure, learn and optimize novelty and diversity of a set of items?" The computational models we develop to answer this question also provide foundational mathematical techniques to throw light on the following three questions: 1. How does one reliably measure the creativity of ideas? 2. How does one form teams to evaluate design ideas? 3. How does one filter good ideas out of hundreds of submissions? Solutions to these questions are key to enable the effective processing of a large collection of design ideas generated in a design contest. In the first part of the dissertation, we discuss key qualities needed in design metrics and propose new diversity and novelty metrics for judging design products. We show that the proposed metrics have higher accuracy and sensitivity compared to existing alternatives in literature. To measure the novelty of a design item, we propose learning from human subjective responses to derive low dimensional triplet embeddings. To measure diversity, we propose an entropy-based diversity metric, which is more accurate and sensitive than benchmarks. In the second part of the dissertation, we introduce the bipartite b-matching problem and argue the need for incorporating diversity in the objective function for matching problems. We propose new submodular and supermodular objective functions to measure diversity and develop multiple matching algorithms for diverse team formation in offline and online cases. Finally, in the third part, we demonstrate filtering and ranking of ideas using diversity metrics based on Determinantal Point Processes as well as submodular functions. In real-world crowd experiments, we demonstrate that such ranking enables increased efficiency in filtering high-quality ideas compared to traditionally used methods