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FutureMatch: Combining human value judgments and machine learning to match in dynamic environments
 In Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI
, 2015
"... The preferred treatment for kidney failure is a transplant; however, demand for donor kidneys far outstrips supply. Kidney exchange, an innovation where willing but incompatible patientdonor pairs can exchange organs—via barter cycles and altruistinitiated chains—provides a lifesaving alternati ..."
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The preferred treatment for kidney failure is a transplant; however, demand for donor kidneys far outstrips supply. Kidney exchange, an innovation where willing but incompatible patientdonor pairs can exchange organs—via barter cycles and altruistinitiated chains—provides a lifesaving alternative. Typically, fielded exchanges act myopically, considering only the current pool of pairs when planning the cycles and chains. Yet kidney exchange is inherently dynamic, with participants arriving and departing. Also, many planned exchange transplants do not go to surgery due to various failures. So, it is important to consider the future when matching. Motivated by our experience running the computational side of a large nationwide kidney exchange, we present FUTUREMATCH, a framework for learning to match in a general dynamic model. FUTUREMATCH takes as input a highlevel objective (e.g., “maximize graft survival of transplants over time”) decided on by experts, then automatically (i) learns based on data how to make this objective concrete and (ii) learns the “means ” to accomplish this goal—a task, in our experience, that humans handle poorly. It uses data from all live kidney transplants in the US since 1987 to learn the quality of each possible match; it then learns the potentials of elements of the current input graph offline (e.g., potentials of pairs based on features such as donor and patient blood types), translates these to weights, and performs a computationally feasible batch matching that incorporates dynamic, failureaware considerations through the weights. We validate FUTUREMATCH on real fielded exchange data. It results in higher values of the objective. Furthermore, even under economically inefficient objectives that enforce equity, it yields better solutions for the efficient objective (which does not incorporate equity) than traditional myopic matching that uses the efficiency objective.
Competing Dynamic Matching Markets
, 2015
"... While dynamic matching markets are usually modeled in isolation, assuming that every agent to be matched enters that market, in many realworld settings there exist rival matching markets with overlapping pools of agents. We extend a framework of dynamic matching due to Akbarpour et al. [2] to char ..."
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While dynamic matching markets are usually modeled in isolation, assuming that every agent to be matched enters that market, in many realworld settings there exist rival matching markets with overlapping pools of agents. We extend a framework of dynamic matching due to Akbarpour et al. [2] to characterize outcomes in cases where two such rival matching markets compete with each other. One market matches quickly while the other builds market thickness by matching slowly. We give an analytic bound on the loss—the expected fraction of unmatched vertices—of this twomarket environment relative to one in which all agents enter either one market or the other, and numerically quantify its exact loss, demonstrating that rival markets increase overall loss compared to a single market that builds thickness. We then look at two competing kidney exchanges, where patients with endstage renal failure swap willing but incompatible donors, and show that matching with rival barter exchanges performs qualitatively the same as matching with rival matching markets—that is, rival markets increase global loss.
Ignorance is Almost Bliss: NearOptimal Stochastic Matching With Few Queries
, 2015
"... The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic kset packing, where the problem is to find a maximum packing of sets, each of which exists with some probability. In this pa ..."
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The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic kset packing, where the problem is to find a maximum packing of sets, each of which exists with some probability. In this paper, we provide edge and set query algorithms for these two problems, respectively, that provably achieve some fraction of the omniscient optimal solution. Our main theoretical result for the stochastic matching (i.e., 2set packing) problem is the design of an adaptive algorithm that queries only a constant number of edges per vertex and achieves a (1 − ) fraction of the omniscient optimal solution, for an arbitrarily small > 0. Moreover, this adaptive algorithm performs the queries in only a constant number of rounds. We complement this result with a nonadaptive (i.e., one round of queries) algorithm that achieves a (0.5 − ) fraction of the omniscient optimum. We also extend both our results to stochastic kset packing by designing an adaptive algorithm that achieves a ( 2 k − ) fraction of the omniscient optimal solution, again with only O(1) queries per element. This guarantee is close to the best known polynomialtime approximation ratio of 3 k+1 − for the deterministic kset packing problem [Fürer and Yu 2013]. We empirically explore the application of (adaptations of) these algorithms to the kidney exchange problem, where patients with endstage renal failure swap willing but incompatible donors. We show on both generated data and on real data from the first 169 match runs of the UNOS nationwide kidney exchange that even a very small number of nonadaptive edge queries per vertex results in large gains in expected successful matches.
Contents
, 2014
"... We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph. We analyze our model from three perspectives: timing, optimization, and information. The main ..."
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We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph. We analyze our model from three perspectives: timing, optimization, and information. The main insight of our analysis is that waiting to thicken the market can be substantially more important than increasing the frequency of transactions, and by characterizing the optimal trade frequency under discounting, we show that this insight is quite robust to the presence of waiting costs. From an optimization perspective, näıve local algorithms, that choose the right time to match agents but do not exploit global network structure, can perform very close to optimal algorithms. From an information perspective, algorithms that employ even shorthorizon information on agents ’ departure times perform substantially better than those that lack such information. To elicit agents ’ departure times, we design an incentivecompatible continuoustime dynamic mechanism without transfers.