336 research outputs found
Almost Optimal Stochastic Weighted Matching With Few Queries
We consider the {\em stochastic matching} problem. An edge-weighted general
(i.e., not necessarily bipartite) graph is given in the input, where
each edge in is {\em realized} independently with probability ; the
realization is initially unknown, however, we are able to {\em query} the edges
to determine whether they are realized. The goal is to query only a small
number of edges to find a {\em realized matching} that is sufficiently close to
the maximum matching among all realized edges. This problem has received a
considerable attention during the past decade due to its numerous real-world
applications in kidney-exchange, matchmaking services, online labor markets,
and advertisements.
Our main result is an {\em adaptive} algorithm that for any arbitrarily small
, finds a -approximation in expectation, by
querying only edges per vertex. We further show that our approach leads
to a -approximate {\em non-adaptive} algorithm that also
queries only edges per vertex. Prior to our work, no nontrivial
approximation was known for weighted graphs using a constant per-vertex budget.
The state-of-the-art adaptive (resp. non-adaptive) algorithm of Maehara and
Yamaguchi [SODA 2018] achieves a -approximation (resp.
-approximation) by querying up to edges per
vertex where denotes the maximum integer edge-weight. Our result is a
substantial improvement over this bound and has an appealing message: No matter
what the structure of the input graph is, one can get arbitrarily close to the
optimum solution by querying only a constant number of edges per vertex.
To obtain our results, we introduce novel properties of a generalization of
{\em augmenting paths} to weighted matchings that may be of independent
interest
Operation Frames and Clubs in Kidney Exchange
A kidney exchange is a centrally-administered barter market where patients
swap their willing yet incompatible donors. Modern kidney exchanges use
2-cycles, 3-cycles, and chains initiated by non-directed donors (altruists who
are willing to give a kidney to anyone) as the means for swapping.
We propose significant generalizations to kidney exchange. We allow more than
one donor to donate in exchange for their desired patient receiving a kidney.
We also allow for the possibility of a donor willing to donate if any of a
number of patients receive kidneys. Furthermore, we combine these notions and
generalize them. The generalization is to exchange among organ clubs, where a
club is willing to donate organs outside the club if and only if the club
receives organs from outside the club according to given specifications. We
prove that unlike in the standard model, the uncapped clearing problem is
NP-complete.
We also present the notion of operation frames that can be used to sequence
the operations across batches, and present integer programming formulations for
the market clearing problems for these new types of organ exchanges.
Experiments show that in the single-donation setting, operation frames
improve planning by 34%--51%. Allowing up to two donors to donate in exchange
for one kidney donated to their designated patient yields a further increase in
social welfare.Comment: Published at IJCAI-1
Diverse Weighted Bipartite b-Matching
Bipartite matching, where agents on one side of a market are matched to
agents or items on the other, is a classical problem in computer science and
economics, with widespread application in healthcare, education, advertising,
and general resource allocation. A practitioner's goal is typically to maximize
a matching market's economic efficiency, possibly subject to some fairness
requirements that promote equal access to resources. A natural balancing act
exists between fairness and efficiency in matching markets, and has been the
subject of much research.
In this paper, we study a complementary goal---balancing diversity and
efficiency---in a generalization of bipartite matching where agents on one side
of the market can be matched to sets of agents on the other. Adapting a
classical definition of the diversity of a set, we propose a quadratic
programming-based approach to solving a supermodular minimization problem that
balances diversity and total weight of the solution. We also provide a scalable
greedy algorithm with theoretical performance bounds. We then define the price
of diversity, a measure of the efficiency loss due to enforcing diversity, and
give a worst-case theoretical bound. Finally, we demonstrate the efficacy of
our methods on three real-world datasets, and show that the price of diversity
is not bad in practice
Scalable Robust Kidney Exchange
In barter exchanges, participants directly trade their endowed goods in a
constrained economic setting without money. Transactions in barter exchanges
are often facilitated via a central clearinghouse that must match participants
even in the face of uncertainty---over participants, existence and quality of
potential trades, and so on. Leveraging robust combinatorial optimization
techniques, we address uncertainty in kidney exchange, a real-world barter
market where patients swap (in)compatible paired donors. We provide two
scalable robust methods to handle two distinct types of uncertainty in kidney
exchange---over the quality and the existence of a potential match. The latter
case directly addresses a weakness in all stochastic-optimization-based methods
to the kidney exchange clearing problem, which all necessarily require explicit
estimates of the probability of a transaction existing---a still-unsolved
problem in this nascent market. We also propose a novel, scalable kidney
exchange formulation that eliminates the need for an exponential-time
constraint generation process in competing formulations, maintains provable
optimality, and serves as a subsolver for our robust approach. For each type of
uncertainty we demonstrate the benefits of robustness on real data from a
large, fielded kidney exchange in the United States. We conclude by drawing
parallels between robustness and notions of fairness in the kidney exchange
setting.Comment: Presented at AAAI1
Allocation Problems in Ride-Sharing Platforms: Online Matching with Offline Reusable Resources
Bipartite matching markets pair agents on one side of a market with agents,
items, or contracts on the opposing side. Prior work addresses online bipartite
matching markets, where agents arrive over time and are dynamically matched to
a known set of disposable resources. In this paper, we propose a new model,
Online Matching with (offline) Reusable Resources under Known Adversarial
Distributions (OM-RR-KAD), in which resources on the offline side are reusable
instead of disposable; that is, once matched, resources become available again
at some point in the future. We show that our model is tractable by presenting
an LP-based adaptive algorithm that achieves an online competitive ratio of 1/2
- eps for any given eps greater than 0. We also show that no non-adaptive
algorithm can achieve a ratio of 1/2 + o(1) based on the same benchmark LP.
Through a data-driven analysis on a massive openly-available dataset, we show
our model is robust enough to capture the application of taxi dispatching
services and ride-sharing systems. We also present heuristics that perform well
in practice.Comment: To appear in AAAI 201
Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity
In bipartite matching problems, vertices on one side of a bipartite graph are
paired with those on the other. In its online variant, one side of the graph is
available offline, while the vertices on the other side arrive online. When a
vertex arrives, an irrevocable and immediate decision should be made by the
algorithm; either match it to an available vertex or drop it. Examples of such
problems include matching workers to firms, advertisers to keywords, organs to
patients, and so on. Much of the literature focuses on maximizing the total
relevance---modeled via total weight---of the matching. However, in many
real-world problems, it is also important to consider contributions of
diversity: hiring a diverse pool of candidates, displaying a relevant but
diverse set of ads, and so on. In this paper, we propose the Online Submodular
Bipartite Matching (\osbm) problem, where the goal is to maximize a submodular
function over the set of matched edges. This objective is general enough to
capture the notion of both diversity (\emph{e.g.,} a weighted coverage
function) and relevance (\emph{e.g.,} the traditional linear function)---as
well as many other natural objective functions occurring in practice
(\emph{e.g.,} limited total budget in advertising settings). We propose novel
algorithms that have provable guarantees and are essentially optimal when
restricted to various special cases. We also run experiments on real-world and
synthetic datasets to validate our algorithms.Comment: To appear in AAAI 201
Who's Thinking? A Push for Human-Centered Evaluation of LLMs using the XAI Playbook
Deployed artificial intelligence (AI) often impacts humans, and there is no
one-size-fits-all metric to evaluate these tools. Human-centered evaluation of
AI-based systems combines quantitative and qualitative analysis and human
input. It has been explored to some depth in the explainable AI (XAI) and
human-computer interaction (HCI) communities. Gaps remain, but the basic
understanding that humans interact with AI and accompanying explanations, and
that humans' needs -- complete with their cognitive biases and quirks -- should
be held front and center, is accepted by the community. In this paper, we draw
parallels between the relatively mature field of XAI and the rapidly evolving
research boom around large language models (LLMs). Accepted evaluative metrics
for LLMs are not human-centered. We argue that many of the same paths tread by
the XAI community over the past decade will be retread when discussing LLMs.
Specifically, we argue that humans' tendencies -- again, complete with their
cognitive biases and quirks -- should rest front and center when evaluating
deployed LLMs. We outline three developed focus areas of human-centered
evaluation of XAI: mental models, use case utility, and cognitive engagement,
and we highlight the importance of exploring each of these concepts for LLMs.
Our goal is to jumpstart human-centered LLM evaluation.Comment: Accepted to CHI 2023 workshop on Generative AI and HC
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