Federated Digital Twin Construction via Distributed Sensing: A Game-Theoretic Online Optimization with Overlapping Coalitions

TL;DR

The paper tackles dynamic federated DT construction by distributing partial-DT creation to edge servers and integrating them at the cloud. It introduces a two-layer hierarchical game (upper-layer two-sided matching and lower-layer overlapping coalition formation) to jointly optimize partial-DT assignments, ES-sensor associations, and resource allocations, with short-term equilibria via Gale-Shapley and SOCF and long-term optimization via a PPO-based DRL framework (DMO). The approach is shown to converge quickly and outperform centralized and non-overlapping baselines across multiple scenarios, highlighting gains in DT quality and cost efficiency. This framework enables scalable, adaptive, and data-silo-resistant DT construction in edge-cloud environments, with potential for real-time, high-fidelity digital replicas of complex physical systems.

Abstract

In this paper, we propose a novel federated framework for constructing the digital twin (DT) model, referring to a living and self-evolving visualization model empowered by artificial intelligence, enabled by distributed sensing under edge-cloud collaboration. In this framework, the DT model to be built at the cloud is regarded as a global one being split into and integrating from multiple functional components, i.e., partial-DTs, created at various edge servers (ESs) using feature data collected by associated sensors. Considering time-varying DT evolutions and heterogeneities among partial-DTs, we formulate an online problem that jointly and dynamically optimizes partial-DT assignments from the cloud to ESs, ES-sensor associations for partial-DT creation, and as well as computation and communication resource allocations for global-DT integration. The problem aims to maximize the constructed DT's model quality while minimizing all induced costs, including energy consumption and configuration costs, in long runs. To this end, we first transform the original problem into an equivalent hierarchical game with an upper-layer two-sided matching game and a lower-layer overlapping coalition formation game. After analyzing these games in detail, we apply the Gale-Shapley algorithm and particularly develop a switch rules-based overlapping coalition formation algorithm to obtain short-term equilibria of upper-layer and lower-layer subgames, respectively. Then, we design a deep reinforcement learning-based solution, called DMO, to extend the result into a long-term equilibrium of the hierarchical game, thereby producing the solution to the original problem. Simulations show the effectiveness of the introduced framework, and demonstrate the superiority of the proposed solution over counterparts.

Figures (9)

• Figure 1: An illustration of the federated DT construction by edge-cloud collaboration. In this framework, the cloud first splits the global DT model into partial-DTs, and then each ES respectively creates its assigned partial-DT using data collected by its associated sensors. Finally all partial-DTs are uploaded to the cloud for global DT integration.
• Figure 2: An illustration of the repeated and hierarchical decision-making process of $\mathcal{G}^H$. Within each time frame $t$, a two-sided matching game $\mathcal{G}^{Up}_t$ acts as the leader to determine partial-DT assignment $x_{c,b}(t)$, and based on this, an overlapping coalition formation game $\mathcal{G}^{Low}_t$ acts as the follower to determine ES-sensor association $y_{b,n}(t)$ and resource allocation decisions $z_{b,n,w}(t)$ and $T_b(t)$.
• Figure 3: Overview of the proposed DMO approach.
• Figure 4: Convergence of the proposed DMO approach.
• Figure 5: Convergence of the designed SOCF algorithm.

Theorems & Definitions (12)

• Definition 1: Two-layer hierarchical game $\mathcal{G}^H$ integrated with $\mathcal{G}^{Up}_{t}$ and $\mathcal{G}^{Low}_t$
• Definition 2: Upper-layer subgame: two-sided matching game $\mathcal{G}^{Up}_{t}$
• Definition 3: Lower-layer subgame: overlapping coalition formation game $\mathcal{G}^{Low}_t$
• Definition 4: Equilibrium of hierarchical game $\mathcal{G}^H$
• Definition 5: Equilibrium of the upper-layer subgame $\mathcal{G}^{Up}_{t}$
• Definition 6: Equilibrium of the lower-layer subgame $\mathcal{G}^{Low}_{t}$
• Lemma 1: Existence of the equilibrium in upper-layer subgame $\mathcal{G}^{Up}_{t}$
• Lemma 2: Existence of the equilibrium in lower-layer subgame $\mathcal{G}^{Low}_{t}$
• Theorem 1: Existence of the equilibrium in hierarchical game $\mathcal{G}^H$
• Definition 7: Overlapping coalition switch rules