The realm of algorithms with predictions has led to the development of several new algorithms that leverage (potentially erroneous) predictions to enhance their performance guarantees. The challenge is to devise algorithms that achieve optimal approximation guarantees as the prediction quality varies from perfect (consistency) to imperfect (robustness). This framework is particularly appealing in mechanism design contexts, where predictions might convey private information about the agents. In this paper, we design strategyproof mechanisms that leverage predictions to achieve improved approximation guarantees for several variants of the Generalized Assignment Problem (GAP) in the private graph model. In this model, first introduced by Dughmi & Ghosh (2010), the set of resources that an agent is compatible with is private information. For the Bipartite Matching Problem (BMP), we give a deterministic group-strategyproof (GSP) mechanism that is $(1 +1/\gamma)$-consistent and $(1 + \gamma)$-robust, where $\gamma \ge 1$ is some confidence parameter. We also prove that this is best possible. Remarkably, our mechanism draws inspiration from the renowned Gale-Shapley algorithm, incorporating predictions as a crucial element. Additionally, we give a randomized mechanism that is universally GSP and improves on the guarantees in expectation. The other GAP variants that we consider all make use of a unified greedy mechanism that adds edges to the assignment according to a specific order. Our universally GSP mechanism randomizes over the greedy mechanism, our mechanism for BMP and the predicted assignment, leading to $(1+3/\gamma)$-consistency and $(3+\gamma)$-robustness in expectation. All our mechanisms also provide more fine-grained approximation guarantees that interpolate between the consistency and the robustness, depending on some natural error measure of the prediction.

翻译：预测算法领域的发展催生了多种利用（可能带有误差的）预测来提升性能保证的新算法。其核心挑战在于设计能在预测质量从完美（一致性）到不完美（鲁棒性）变化时仍实现最优近似保证的算法。该框架在机制设计场景中尤其具有吸引力——预测可能隐含参与者的私有信息。本文针对私有图模型中的广义分配问题（GAP）变体，设计了一类利用预测来改进近似保证的策略证明机制。在由Dughmi与Ghosh（2010）首次提出的该模型中，代理可兼容的资源集属于私有信息。对于二部图匹配问题（BMP），我们给出一个确定性的群体策略证明（GSP）机制，其具有(1+1/γ)-一致性与(1+γ)-鲁棒性（γ≥1为置信参数），并证明该结果是最优的。值得注意的是，该机制从经典Gale-Shapley算法中汲取灵感，将预测作为关键要素。此外，我们提出一个通用GSP随机机制，在期望意义上改进了保证。其余GAP变体均采用统一贪心机制——按特定顺序向分配中添加边。我们提出的通用GSP机制通过对贪心机制、BMP机制与预测分配进行随机化，在期望意义上实现了(1+3/γ)-一致性与(3+γ)-鲁棒性。所有机制还根据预测的某种自然误差度量，提供了在一致性与鲁棒性之间插值的更精细近似保证。