22 research outputs found
School Choice as a One-Sided Matching Problem: Cardinal Utilities and Optimization
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. Previously considered criteria for evaluating proposed mechanisms such as stability, strategyproofness and Pareto efficiency do not always translate into desirable student assignments. In this note, we explore a class of one-sided, cardinal utility maximizing matching mechanisms focused exclusively on student preferences. We adapt a well-known combinatorial optimization technique (the Hungarian algorithm) as the kernel of this class of matching mechanisms. We find that, while such mechanisms can be adapted to meet desirable criteria not met by any previously employed mechanism in the school choice literature, they are not strategyproof. We discuss the practical implications and limitations of our approach at the end of the article
Adapting a Kidney Exchange Algorithm to Align with Human Values
The efficient and fair allocation of limited resources is a classical problem
in economics and computer science. In kidney exchanges, a central market maker
allocates living kidney donors to patients in need of an organ. Patients and
donors in kidney exchanges are prioritized using ad-hoc weights decided on by
committee and then fed into an allocation algorithm that determines who gets
what--and who does not. In this paper, we provide an end-to-end methodology for
estimating weights of individual participant profiles in a kidney exchange. We
first elicit from human subjects a list of patient attributes they consider
acceptable for the purpose of prioritizing patients (e.g., medical
characteristics, lifestyle choices, and so on). Then, we ask subjects
comparison queries between patient profiles and estimate weights in a
principled way from their responses. We show how to use these weights in kidney
exchange market clearing algorithms. We then evaluate the impact of the weights
in simulations and find that the precise numerical values of the weights we
computed matter little, other than the ordering of profiles that they imply.
However, compared to not prioritizing patients at all, there is a significant
effect, with certain classes of patients being (de)prioritized based on the
human-elicited value judgments
Certifying Solvers for Clique and Maximum Common (Connected) Subgraph Problems
An algorithm is said to be certifying if it outputs, together with a solution to the problem it solves, a proof that this solution is correct. We explain how state of the art maximum clique, maximum weighted clique, maximal clique enumeration and maximum common (connected) induced subgraph algorithms can be turned into certifying solvers by using pseudo-Boolean models and cutting planes proofs, and demonstrate that this approach can also handle reductions between problems. The generality of our results suggests that this method is ready for widespread adoption in solvers for combinatorial graph problems
Active classification with comparison queries
We study an extension of active learning in which the learning algorithm may
ask the annotator to compare the distances of two examples from the boundary of
their label-class. For example, in a recommendation system application (say for
restaurants), the annotator may be asked whether she liked or disliked a
specific restaurant (a label query); or which one of two restaurants did she
like more (a comparison query).
We focus on the class of half spaces, and show that under natural
assumptions, such as large margin or bounded bit-description of the input
examples, it is possible to reveal all the labels of a sample of size using
approximately queries. This implies an exponential improvement over
classical active learning, where only label queries are allowed. We complement
these results by showing that if any of these assumptions is removed then, in
the worst case, queries are required.
Our results follow from a new general framework of active learning with
additional queries. We identify a combinatorial dimension, called the
\emph{inference dimension}, that captures the query complexity when each
additional query is determined by examples (such as comparison queries,
each of which is determined by the two compared examples). Our results for half
spaces follow by bounding the inference dimension in the cases discussed above.Comment: 23 pages (not including references), 1 figure. The new version
contains a minor fix in the proof of Lemma 4.
Understanding and Addressing the Pitfalls of Bisimulation-based Representations in Offline Reinforcement Learning
While bisimulation-based approaches hold promise for learning robust state
representations for Reinforcement Learning (RL) tasks, their efficacy in
offline RL tasks has not been up to par. In some instances, their performance
has even significantly underperformed alternative methods. We aim to understand
why bisimulation methods succeed in online settings, but falter in offline
tasks. Our analysis reveals that missing transitions in the dataset are
particularly harmful to the bisimulation principle, leading to ineffective
estimation. We also shed light on the critical role of reward scaling in
bounding the scale of bisimulation measurements and of the value error they
induce. Based on these findings, we propose to apply the expectile operator for
representation learning to our offline RL setting, which helps to prevent
overfitting to incomplete data. Meanwhile, by introducing an appropriate reward
scaling strategy, we avoid the risk of feature collapse in representation
space. We implement these recommendations on two state-of-the-art
bisimulation-based algorithms, MICo and SimSR, and demonstrate performance
gains on two benchmark suites: D4RL and Visual D4RL. Codes are provided at
\url{https://github.com/zanghyu/Offline_Bisimulation}.Comment: NeurIPS 202