  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.
