arXiv subjects

Hau Chan

Publications and source records attributed to Hau Chan.

At least 19 recordsLinked to original sources

arXiv2026

Strategyproof Mechanisms for Connecting Impassable Regions

We study strategyproof mechanisms for building a pathway between two regions of a line segment separated by an obstacle. Each of the $n$ agents has a private location within its region and may use either its original route to a facility or the new pathway, whose traversal cost is a fraction $k\in[0,1)$ of its length. We seek strategyproof (SP) and group-strategyproof (GSP) mechanisms that approximately minimize maximum cost or social cost. After characterizing optimal pathways for both objectives, we establish a tight deterministic maximum-cost approximation ratio of $\frac{2}{1+k}$ and a deterministic social-cost upper bound of $\frac{n}{1+k(n-1)}$, together with complementary lower bounds. Both upper bounds are achieved by GSP mechanisms. We then study randomized mechanisms under strategyproofness in expectation. A power-proportional mechanism achieves a social-cost approximation ratio at most $5$, independent of $n$ and $k$, with a tight guarantee of $3$ for this mechanism when $k=0$. We prove randomized lower bounds of $\frac{3+2k}{2+3k}$ for maximum cost and $\max\big\{1,\frac{285}{263+385k}\big\}$ for social cost, the latter for $n\ge7$. Finally, we improve several bounds for the real-line pathway model of [Chan and Wang, AAMAS 2023]. Our deterministic maximum-cost lower bound of $2$ matches the upper bound obtainable from [Qin, Fang, and Liu, COCOA 2024]. We strengthen the deterministic social-cost lower bound from $\frac32$ to $2$ under SP and to $\max\{2,n-1\}$ under GSP. For randomized social cost, we sharpen the guarantee of Chan and Wang's proportional mechanism from $6$ to $3$ and raise their lower bound from $1.02$ to $\frac{285}{263}\approx1.08365$ for $n\ge7$.

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arXiv2026

Improved Randomized Approximations for Strategic Obnoxious Facility Location

We study randomized strategyproof mechanisms for strategic obnoxious facility location on a line segment, where agents wish the facility to be located as far away from them as possible and their utility is their distance from the facility, under the social utility and minimum utility objectives. For social utility, we propose a novel randomized mechanism that breaks the previously best known $\frac32$-approximation of [Cheng, Yu, and Zhang, TCS 2013], achieving an approximation ratio of at most $1.47359$. We also raise the lower bound on the approximation ratio of randomized strategyproof mechanisms from $\frac{2}{\sqrt{3}}\approx1.15470$ [Feigenbaum et al., JAAMAS 2020] to $\frac{105}{88}\approx1.19318$. For minimum utility, following the profile-independent approach of [Chan, Lin and Wang, AAMAS 2026], we design a simple randomized mechanism that reduces the approximation guarantee from $\sqrt{2n}+O(1)$ to $\sqrt n+O(1)$, where $n$ is the number of agents. Finally, we prove that no randomized strategyproof mechanism can achieve an asymptotic approximation ratio strictly smaller than $2$, strengthening the previous asymptotic lower bound of $\frac32$ [Feigenbaum et al., JAAMAS 2020]. Thus, all four bounds considered in this paper strictly improve upon the corresponding previously known results.

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arXiv2026

Guiding Worker Self-Selection in Crowdsourcing Contests: An LLM-Augmented Algorithmic Approach

Crowdsourcing platforms coordinate large pools of online workers who strategically choose which contests to enter and how much effort to invest. This self-selection can leave important contests with too few participants or too little effort, while workers may regret entering contests that leave them worse off than available alternatives. We study how platforms can recommend contests to workers using self-selection in Tullock contests (SSTC), a two-stage model in which workers first choose contests and then compete within them. We introduce GRAF, a greedy polynomial-time framework that constructs self-selection outcomes by ordering workers according to a score vector, with guarantees of zero worker regret and platform optimality in special cases of SSTC. Because effective orderings are difficult to design under worker heterogeneity, we propose LLMScore, an LLM-driven evolutionary framework that automatically designs GRAF's scoring algorithm. LLMScore addresses two challenges: jointly optimizing platform utility and worker satisfaction, and evaluating worker regret when exact computation is intractable. Trained only on small instances of one setting, it transfers to larger and structurally different settings; moreover, its output is human-readable code that platform operators can inspect and modify. Across 1,000 synthetic instances spanning four settings, GRAF with LLMScore consistently achieves high-quality, often near-optimal, outcomes with low worker regret, benefiting both platforms and workers.

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arXiv2026

Randomized Strategyproof Facility Location: Two Facilities and Beyond

We design and analyze randomized strategyproof mechanisms for multi-facility location under the utilitarian social-cost objective, the sum of the agents' distances to their nearest facilities. For two facilities, the Pairwise-Distance mechanism locates facilities at a pair of reported locations sampled with probability proportional to their distance. It is strategyproof on Ptolemaic spaces, including Euclidean and Hilbert spaces as special cases, and has an approximation ratio of $4$. The resulting Hybrid-Distance mechanism is a fixed-probability mixture: it selects the classical Proportional mechanism [Lu et al., EC'10] with probability $\lambda^*=\frac{5+4\sqrt3}{23}$ and Pairwise-Distance with probability $1-\lambda^*$. It is strategyproof on Ptolemaic spaces and has a tight approximation ratio of $\frac{74+4\sqrt3}{23}\approx3.5186$, breaking the long-standing factor-$4$ benchmark of [Lu et al., EC'10]. We complement the two-facility results by studying more facilities. First, for $n$ agents and $k=n-1$ facilities, we introduce the Inverse-Square mechanism, which omits one report with probability proportional to the inverse square of its nearest-neighbor distance and locates facilities at all remaining reports. It is strategyproof on any metric space and has an approximation ratio of $\Theta(\sqrt{n})$, improving the previous best-known ratio of $\frac{n}{2}$ [Escoffier et al., ADT'11]. Second, for $k$ facilities on the line, we introduce the Gap-Product mechanism, which locates facilities at $k$ reports and weights each set by the product of the gaps between consecutive selected reports. When $k=3$, it is strategyproof and has a $6$-approximation, replacing the previous $n$-dependent guarantee [Fotakis and Tzamos, EC'13] by a constant, whereas it is not strategyproof for any $k\ge4$.

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arXiv2026

Improved Metric Distortion Bounds for Deterministic Weighted-Tournament Voting Rules

In metric social choice, voters and candidates lie in a common but unknown metric space, voters rank candidates by distance, and a voting rule seeks to minimize total distance to the voters. Its distortion is the worst-case approximation ratio relative to the minimum possible total distance. We study weighted-tournament rules (also known as C2 rules), which observe only the fraction of voters who prefer $a$ to $b$ for each pair of candidates $a,b$. These frequencies form a weighted tournament on candidates, a compressed representation that omits voter identities and the association of comparisons with individual voters. Prior work placed the optimal distortion of deterministic C2 rules between $3.1128$ and $3.9312$ [Charikar et al., EC 2025]. We introduce the Path-Unblanketed Set rule, a polynomial-time deterministic C2 rule with distortion at most $1+2\sqrt{2}\approx3.8284$ for every finite number of candidates. For elections with no more than six candidates, we prove with computer assistance that the distortion is at most $3.3346$. Furthermore, using an exact computer-assisted certificate, we provide a lower bound of $3.1828$ for deterministic C2 rules as a byproduct.

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arXiv2026

Strategyproof Mechanisms for Euclidean Facility Location Problems under $L_p$-norm Social Cost

We study strategyproof mechanisms for eliciting agents' location preferences truthfully in the Euclidean plane $\mathbb R^2$ and locating a facility so as to minimize the $L_p$-norm social cost, defined as the $L_p$-norm of the vector of distances from the facility to the agents' preferred locations, for any $p \ge 1$. While the cases $p=1$ and $p=\infty$ have been well-studied, open questions remain about the optimal approximation ratios achievable by strategyproof mechanisms for general $p$. Our first result resolves an open question of Goel and Hann-Caruthers [Soc. Choice Welf. 2023]. They showed that the coordinate-wise median (CM) mechanism achieves an approximation ratio lying between $2^{1-\frac{1}{p}}$ and $2^{\frac{3}{2}-\frac{2}{p}}$ for $p\ge 2$, and they conjectured that it is exactly $2^{1-\frac{1}{p}}$. We confirm this conjecture, and we further show that CM has a tight $\sqrt 2$-approximation for $1\le p\le 2$. Since it is previously known that the CM mechanism has the optimal approximation ratio among all deterministic anonymous strategyproof mechanisms for all $p\ge 1$, we complete the picture of deterministic mechanisms. Our second and third results demonstrate that two randomized mechanisms can yield better approximation ratios. In particular, we first consider the uniformly rotated coordinate-wise median (URCM) mechanism, and prove that, for $1\le p<2$, its approximation ratio strictly improves over the deterministic bound $\sqrt{2}$, while no such improvement is possible for $p\ge 2$. We then study the centroid random dictatorship mechanism that returns the average location (i.e., centroid) and the random dictatorship each with half probability, and show that its approximation ratio strictly improves over CM and URCM for every finite $p\gtrsim 1.6$.

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arXiv2026

Mechanism Design for Connecting Regions Under Disruptions

Man-made and natural disruptions such as planned constructions on roads, suspensions of bridges, and blocked roads by trees/mudslides/floods can often create obstacles that separate two connected regions. As a result, the traveling and reachability of agents from their respective regions to other regions can be affected. To minimize the impact of the obstacles and maintain agent accessibility, we initiate the problem of constructing a new pathway (e.g., a detour or new bridge) connecting the regions disconnected by obstacles from the mechanism design perspective. In the problem, each agent in their region has a private location and is required to access the other region. The cost of an agent is the distance from their location to the other region via the pathway. Our goal is to design strategyproof mechanisms that elicit truthful locations from the agents and approximately optimize the social or maximum cost of agents by determining locations in the regions for building a pathway. We provide a characterization of all strategyproof and anonymous mechanisms. For the social and maximum costs, we provide upper and lower bounds on the approximation ratios of strategyproof mechanisms.

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arXiv2026

Large Language Models for Designing Participatory Budgeting Rules

Participatory budgeting (PB) is a democratic paradigm for deciding the funding of public projects given the residents' preferences, which has been adopted in numerous cities across the world. The main focus of PB is designing rules, functions that return feasible budget allocations for a set of projects subject to some budget constraint. Designing PB rules that optimize both utility and fairness objectives based on agent preferences had been challenging due to the extensive domain knowledge required and the proven trade-off between the two notions. Recently, large language models (LLMs) have been increasingly employed for automated algorithmic design. Given the resemblance of PB rules to algorithms for classical knapsack problems, in this paper, we introduce a novel framework, named LLMRule, that addresses the limitations of existing works by incorporating LLMs into an evolutionary search procedure for automating the design of PB rules. Our experimental results, evaluated on more than 600 real-world PB instances obtained from the U.S., Canada, Poland, and the Netherlands with different representations of agent preferences, demonstrate that the LLM-generated rules generally outperform existing handcrafted rules in terms of overall utility while still maintaining a similar degree of fairness.

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arXiv2025

Obnoxious Facility Location Problems: Strategyproof Mechanisms Optimizing $L_p$-Aggregated Utilities and Costs

We study the problem of locating a single obnoxious facility on the normalized line segment $[0,1]$ with strategic agents from a mechanism design perspective. Each agent has a preference for the undesirable location of the facility and would prefer the facility to be far away from their location. We consider the utility of the agent, defined as the distance between the agent's location and the facility location, and the cost of each agent, equal to one minus the utility. Given this standard setting of obnoxious facility location problems, our goal is to design (group) strategyproof mechanisms to elicit agent locations truthfully and determine facility location approximately optimizing the $L_p$-aggregated utility and cost objectives, which generalizes the $L_p$-norm ($p\ge 1$) of the agents' utilities and agents' costs to any $p \in [-\infty, \infty]$, respectively. We establish upper and lower bounds on the approximation ratios of deterministic and randomized (group) strategyproof mechanisms for maximizing the $L_p$-aggregated utilities or minimizing the $L_p$-aggregated costs across the range of $p$-values. While there are gaps between upper and lower bounds for randomized mechanisms, our bounds for deterministic mechanisms are tight.

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arXiv2025

Centralized Group Equitability and Individual Envy-Freeness in the Allocation of Indivisible Items

We study the fair allocation of indivisible items for groups of agents from the perspectives of the agents and a centralized allocator. In our setting, the centralized allocator is interested in ensuring the allocation is fair among the groups and between agents. This setting applies to many real-world scenarios, including when a school administrator wants to allocate resources (e.g., office spaces and supplies) to staff members in departments and when a city council allocates limited housing units to various families in need across different communities. To ensure fair allocation between agents, we consider the classical envy-freeness (EF) notion. To ensure fairness among the groups, we define the notion of centralized group equitability (CGEQ) to capture the fairness for the groups from the allocator's perspective. Because an EF or CGEQ allocation does not always exist in general, we consider their corresponding natural relaxations of envy-freeness to one item (EF1) and centralized group equitability up to one item (CGEQ1). For different classes of valuation functions of the agents and the centralized allocator, we show that allocations satisfying both EF1 and CGEQ1 always exist and design efficient algorithms to compute these allocations. We also consider the centralized group maximin share (CGMMS) from the centralized allocator's perspective as a group-level fairness objective with EF1 for agents and present several results.

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arXiv2025

Strategyproof Facility Location with Prediction: Minimizing the Maximum Cost

We study the mechanism design problem of facility location on a metric space in the learning-augmented framework, where mechanisms have access to imperfect predictions of the optimal facility locations. Our objective is to design strategyproof (SP) mechanisms that truthfully elicit agents' preferences over facility locations and, using the given prediction, select a facility location that approximately minimizes the maximum cost among all agents. In particular, we seek SP mechanisms whose approximation guarantees depend on the prediction error: they should achieve improved performance when the prediction is accurate (the property of \emph{consistency}) while still ensuring strong worst-case guarantees when the prediction is arbitrarily inaccurate (the property of \emph{robustness}). On the real line, we characterize all deterministic SP mechanisms with consistency strictly better than 2 and bounded robustness for the maximum cost. We show that any such mechanism must coincide with the MinMaxP mechanism, which returns the prediction if it lies between the two extreme agent locations and otherwise returns the agent location closest to the prediction. For any prediction error $\eta\ge 0$, we prove that MinMaxP achieves a $(1+\min(1, \eta))$-approximation and that no deterministic SP mechanism can obtain a better approximation ratio. In addition, for two-dimensional spaces with the $\ell_p$ distance, we analyze the approximation guarantees of a deterministic mechanism that applies MinMaxP independently on each coordinate, as well as a randomized mechanism that selects between two deterministic mechanisms with carefully chosen probabilities. We further extend these results to the $L_p$-norm social cost objective on the line metric and the maximum cost objective on the tree metric. Finally, we examine the group strategyproofness of the mechanisms.

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arXiv2025

RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models

Solving NP-hard combinatorial optimization problems (COPs) (e.g., traveling salesman problems (TSPs) and capacitated vehicle routing problems (CVRPs)) in practice traditionally involves handcrafting heuristics or specifying a search space for finding effective heuristics. The main challenges from these approaches, however, are the sheer amount of domain knowledge and implementation efforts required from human experts. Recently, significant progress has been made to address these challenges, particularly by using large language models (LLMs) to design heuristics within some predetermined generalized algorithmic framework (GAF, e.g., ant colony optimization and guided local search) for building key functions/components (e.g., a priori information on how promising it is to include each edge in a solution for TSP and CVRP). Although existing methods leveraging this idea have shown to yield impressive optimization performance, they are not fully end-to-end and still require considerable manual interventions. In this paper, we propose a novel end-to-end framework, named RedAHD, that enables these LLM-based heuristic design methods to operate without the need of GAFs. More specifically, RedAHD employs LLMs to automate the process of reduction, i.e., transforming the COP at hand into similar COPs that are better-understood, from which LLM-based heuristic design methods can design effective heuristics for directly solving the transformed COPs and, in turn, indirectly solving the original COP. Our experimental results, evaluated on six COPs, show that RedAHD is capable of designing heuristics with competitive or improved results over the state-of-the-art methods with minimal human involvement.

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arXiv2025

Distance Preservation Games

We introduce and analyze distance preservation games (DPGs). In DPGs, agents express ideal distances to other agents and need to choose locations in the unit interval while preserving their ideal distances as closely as possible. We analyze the existence and computation of location profiles that are jump stable (i.e., no agent can benefit by moving to another location) or welfare optimal for DPGs, respectively. Specifically, we prove that there are DPGs without jump stable location profiles and identify important cases where such outcomes always exist and can be computed efficiently. Similarly, we show that finding welfare optimal location profiles is NP-complete and present approximation algorithms for finding solutions with social welfare close to optimal. Finally, we prove that DPGs have a price of anarchy of at most $2$.

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arXiv2025

CARE: Compatibility-Aware Incentive Mechanisms for Federated Learning with Budgeted Requesters

Federated learning (FL) is a promising approach that allows requesters (\eg, servers) to obtain local training models from workers (e.g., clients). Since workers are typically unwilling to provide training services/models freely and voluntarily, many incentive mechanisms in FL are designed to incentivize participation by offering monetary rewards from requesters. However, existing studies neglect two crucial aspects of real-world FL scenarios. First, workers can possess inherent incompatibility characteristics (e.g., communication channels and data sources), which can lead to degradation of FL efficiency (e.g., low communication efficiency and poor model generalization). Second, the requesters are budgeted, which limits the amount of workers they can hire for their tasks. In this paper, we investigate the scenario in FL where multiple budgeted requesters seek training services from incompatible workers with private training costs. We consider two settings: the cooperative budget setting where requesters cooperate to pool their budgets to improve their overall utility and the non-cooperative budget setting where each requester optimizes their utility within their own budgets. To address efficiency degradation caused by worker incompatibility, we develop novel compatibility-aware incentive mechanisms, CARE-CO and CARE-NO, for both settings to elicit true private costs and determine workers to hire for requesters and their rewards while satisfying requester budget constraints. Our mechanisms guarantee individual rationality, truthfulness, budget feasibility, and approximation performance. We conduct extensive experiments using real-world datasets to show that the proposed mechanisms significantly outperform existing baselines.

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arXiv2025

Large Language Models for Multi-Facility Location Mechanism Design

Designing strategyproof mechanisms for multi-facility location that optimize social costs based on agent preferences had been challenging due to the extensive domain knowledge required and poor worst-case guarantees. Recently, deep learning models have been proposed as alternatives. However, these models require some domain knowledge and extensive hyperparameter tuning as well as lacking interpretability, which is crucial in practice when transparency of the learned mechanisms is mandatory. In this paper, we introduce a novel approach, named LLMMech, that addresses these limitations by incorporating large language models (LLMs) into an evolutionary framework for generating interpretable, hyperparameter-free, empirically strategyproof, and nearly optimal mechanisms. Our experimental results, evaluated on various problem settings where the social cost is arbitrarily weighted across agents and the agent preferences may not be uniformly distributed, demonstrate that the LLM-generated mechanisms generally outperform existing handcrafted baselines and deep learning models. Furthermore, the mechanisms exhibit impressive generalizability to out-of-distribution agent preferences and to larger instances with more agents.

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arXiv2024

Double Oracle Neural Architecture Search for Game Theoretic Deep Learning Models

In this paper, we propose a new approach to train deep learning models using game theory concepts including Generative Adversarial Networks (GANs) and Adversarial Training (AT) where we deploy a double-oracle framework using best response oracles. GAN is essentially a two-player zero-sum game between the generator and the discriminator. The same concept can be applied to AT with attacker and classifier as players. Training these models is challenging as a pure Nash equilibrium may not exist and even finding the mixed Nash equilibrium is difficult as training algorithms for both GAN and AT have a large-scale strategy space. Extending our preliminary model DO-GAN, we propose the methods to apply the double oracle framework concept to Adversarial Neural Architecture Search (NAS for GAN) and Adversarial Training (NAS for AT) algorithms. We first generalize the players' strategies as the trained models of generator and discriminator from the best response oracles. We then compute the meta-strategies using a linear program. For scalability of the framework where multiple network models of best responses are stored in the memory, we prune the weakly-dominated players' strategies to keep the oracles from becoming intractable. Finally, we conduct experiments on MNIST, CIFAR-10 and TinyImageNet for DONAS-GAN. We also evaluate the robustness under FGSM and PGD attacks on CIFAR-10, SVHN and TinyImageNet for DONAS-AT. We show that all our variants have significant improvements in both subjective qualitative evaluation and quantitative metrics, compared with their respective base architectures.

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arXiv2024

Mechanism Design for Extending the Accessibility of Facilities

We study a variation of facility location problems (FLPs) that aims to improve the accessibility of agents to the facility within the context of mechanism design without money. In such a variation, agents have preferences on the ideal locations of the facility on a real line, and the facility's location is fixed in advance where (re)locating the facility is not possible due to various constraints (e.g., limited space and construction costs). To improve the accessibility of agents to facilities, existing mechanism design literature in FLPs has proposed to structurally modify the real line (e.g., by adding a new interval) or provide shuttle services between two points when structural modifications are not possible. In this paper, we focus on the latter approach and propose to construct an accessibility range to extend the accessibility of the facility. In the range, agents can receive accommodations (e.g., school buses, campus shuttles, or pickup services) to help reach the facility. Therefore, the cost of each agent is the distance from their ideal location to the facility (possibility) through the range. We focus on designing strategyproof mechanisms that elicit true ideal locations from the agents and construct accessibility ranges (intervals) to approximately minimize the social cost or the maximum cost of agents. For both social and maximum costs, we design group strategyproof mechanisms with asymptotically tight bounds on the approximation ratios.

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arXiv2024

In-Context Exploiter for Extensive-Form Games

Nash equilibrium (NE) is a widely adopted solution concept in game theory due to its stability property. However, we observe that the NE strategy might not always yield the best results, especially against opponents who do not adhere to NE strategies. Based on this observation, we pose a new game-solving question: Can we learn a model that can exploit any, even NE, opponent to maximize their own utility? In this work, we make the first attempt to investigate this problem through in-context learning. Specifically, we introduce a novel method, In-Context Exploiter (ICE), to train a single model that can act as any player in the game and adaptively exploit opponents entirely by in-context learning. Our ICE algorithm involves generating diverse opponent strategies, collecting interactive history training data by a reinforcement learning algorithm, and training a transformer-based agent within a well-designed curriculum learning framework. Finally, comprehensive experimental results validate the effectiveness of our ICE algorithm, showcasing its in-context learning ability to exploit any unknown opponent, thereby positively answering our initial game-solving question.

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