arXiv subjects

Yiheng Shen

Publications and source records attributed to Yiheng Shen.

25 records · Page 2Linked to original sources

arXiv2023

Fair Multiwinner Elections with Allocation Constraints

We consider the multiwinner election problem where the goal is to choose a committee of $k$ candidates given the voters' utility functions. We allow arbitrary additional constraints on the chosen committee, and the utilities of voters to belong to a very general class of set functions called $β$-self bounding. When $β=1$, this class includes XOS (and hence, submodular and additive) utilities. We define a novel generalization of core stability called restrained core to handle constraints and consider multiplicative approximations on the utility under this notion. Our main result is the following: If a smooth version of Nash Welfare is globally optimized over committees within the constraints, the resulting committee lies in the $e^β$-approximate restrained core for $β$-self bounding utilities and arbitrary constraints. As a result, we obtain the first constant approximation for stability with arbitrary additional constraints even for additive utilities (factor of $e$), and the first analysis of the stability of Nash Welfare with XOS functions even with no constraints. We complement this positive result by showing that the $c$-approximate restrained core can be empty for $c<16/15$ even for approval utilities and one additional constraint. Furthermore, the exponential dependence on $β$ in the approximation is unavoidable for $β$-self bounding functions even with no constraints. We next present improved and tight approximation results for simpler classes of utility functions and simpler types of constraints. We also present an extension of restrained core to extended justified representation with constraints and show an existence result for matroid constraints. We finally generalize our results to the setting with arbitrary-size candidates and no additional constraints. Our techniques are different from previous analyses and are of independent interest.

cs.GT↗

arXiv2021

Approximate Core for Committee Selection via Multilinear Extension and Market Clearing

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an $α$ factor. If no blocking committee exists under this definition, we call this an $α$-core. Our main result is that an $α$-core, for $α< 67.37$, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to $α< 9.27$ for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of $α> 1.015$ for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.

cs.GT↗

arXiv2021

Targeting Makes Sample Efficiency in Auction Design

This paper introduces the targeted sampling model in optimal auction design. In this model, the seller may specify a quantile interval and sample from a buyer's prior restricted to the interval. This can be interpreted as allowing the seller to, for example, examine the top $40$ percents bids from previous buyers with the same characteristics. The targeting power is quantified with a parameter $Δ\in [0, 1]$ which lower bounds how small the quantile intervals could be. When $Δ= 1$, it degenerates to Cole and Roughgarden's model of i.i.d. samples; when it is the idealized case of $Δ= 0$, it degenerates to the model studied by Chen et al. (2018). For instance, for $n$ buyers with bounded values in $[0, 1]$, $\tilde{O}(ε^{-1})$ targeted samples suffice while it is known that at least $\tildeΩ(n ε^{-2})$ i.i.d. samples are needed. In other words, targeted sampling with sufficient targeting power allows us to remove the linear dependence in $n$, and to improve the quadratic dependence in $ε^{-1}$ to linear. In this work, we introduce new technical ingredients and show that the number of targeted samples sufficient for learning an $ε$-optimal auction is substantially smaller than the sample complexity of i.i.d. samples for the full spectrum of $Δ\in [0, 1)$. Even with only mild targeting power, i.e., whenever $Δ= o(1)$, our targeted sample complexity upper bounds are strictly smaller than the optimal sample complexity of i.i.d. samples.

cs.GT↗

arXiv2020

Truthful Data Acquisition via Peer Prediction

We consider the problem of purchasing data for machine learning or statistical estimation. The data analyst has a budget to purchase datasets from multiple data providers. She does not have any test data that can be used to evaluate the collected data and can assign payments to data providers solely based on the collected datasets. We consider the problem in the standard Bayesian paradigm and in two settings: (1) data are only collected once; (2) data are collected repeatedly and each day's data are drawn independently from the same distribution. For both settings, our mechanisms guarantee that truthfully reporting one's dataset is always an equilibrium by adopting techniques from peer prediction: pay each provider the mutual information between his reported data and other providers' reported data. Depending on the data distribution, the mechanisms can also discourage misreports that would lead to inaccurate predictions. Our mechanisms also guarantee individual rationality and budget feasibility for certain underlying distributions in the first setting and for all distributions in the second setting.

cs.GT↗

arXiv2020

A Study on the Splitting Strategy of Server Resources

The paper is based on Noar's model of charged queues. We extend this model into multi-server systems with information about length and service rate disclosed for all the customers, and the customers can choose the optimal options. We discuss whether the splitting strategy of the server resource could bring more revenue for the service provider. We prove that any G/D/1 server supplier cannot earn more revenue by splitting his resource under the equal-toll limitations.

math.PR↗

arXiv2020

New Complexity Results on Coalitional Manipulation of Borda

The Borda voting rule is a positional scoring rule for $z$ candidates such that in each vote, the first candidate receives $z-1$ points, the second $z-2$ points and so on. The winner in the Borda rule is the candidate with highest total score. We study the manipulation problem of the Borda rule in a setting with two non-manipulators while one of the non-manipulator's vote is weighted. We demonstrate a sharp contrast on computational complexity depending on the weight of the non-manipulator: the problem is NP-hard when the weight is larger than $1$ while there exists an efficient algorithm to find a manipulation when the weight is at most $1$.

cs.GT↗

arXiv2020

Mechanism Design for Multi-Party Machine Learning

In a multi-party machine learning system, different parties cooperate on optimizing towards better models by sharing data in a privacy-preserving way. A major challenge in learning is the incentive issue. For example, if there is competition among the parties, one may strategically hide his data to prevent other parties from getting better models. In this paper, we study the problem through the lens of mechanism design and incorporate the features of multi-party learning in our setting. First, each agent's valuation has externalities that depend on others' types and actions. Second, each agent can only misreport a type lower than his true type, but not the other way round. We call this setting interdependent value with type-dependent action spaces. We provide the optimal truthful mechanism in the quasi-monotone utility setting. We also provide necessary and sufficient conditions for truthful mechanisms in the most general case. Finally, we show the existence of such mechanisms is highly affected by the market growth rate and provide empirical analysis.

cs.MA↗