Jianan Lin

Hau Chan, Jianan Lin, Chenhao Wang

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 $η\ge 0$, we prove that MinMaxP achieves a $(1+\min(1, η))$-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.

Hau Chan, Jianan Lin, Zining Qin et al.

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.

Li Zhang, Zhongxuan Han, XiaoHua Feng et al.

Efficient and lightweight adaptation of pre-trained Vision-Language Models (VLMs) to downstream tasks through collaborative interactions between local clients and a central server is a rapidly emerging research topic in federated learning. Existing adaptation algorithms are typically trained iteratively, which incur significant communication costs and increase the susceptibility to potential attacks. Motivated by the one-shot federated training techniques that reduce client-server exchanges to a single round, developing a lightweight one-shot federated VLM adaptation method to alleviate these issues is particularly attractive. However, current one-shot approaches face certain challenges in adapting VLMs within federated settings: (1) insufficient exploitation of the rich multimodal information inherent in VLMs; (2) lack of specialized adaptation strategies to systematically handle the severe data heterogeneity; and (3) requiring additional training resource of clients or server. To bridge these gaps, we propose a novel Training-free One-shot Federated Adaptation framework for VLMs, named TOFA. To fully leverage the generalizable multimodal features in pre-trained VLMs, TOFA employs both visual and textual pipelines to extract task-relevant representations. In the visual pipeline, a hierarchical Bayesian model learns personalized, class-specific prototype distributions. For the textual pipeline, TOFA evaluates and globally aligns the generated local text prompts for robustness. An adaptive weight calibration mechanism is also introduced to combine predictions from both modalities, balancing personalization and robustness to handle data heterogeneity. Our method is training-free, not relying on additional training resources on either the client or server side. Extensive experiments across 9 datasets in various federated settings demonstrate the effectiveness of the proposed TOFA method.