Human digital twin (HDT) is an emerging paradigm that bridges physical twins (PTs) with powerful virtual twins (VTs) for assisting complex task executions in human-centric services. In this paper, we study a two-timescale online optimization for building HDT under an end-edge-cloud collaborative framework. As a unique feature of HDT, we consider that PTs' corresponding VTs are deployed on edge servers, consisting of not only generic models placed by downloading experiential knowledge from the cloud but also customized models updated by collecting personalized data from end devices. To maximize task execution accuracy with stringent energy and delay constraints, and by taking into account HDT's inherent mobility and status variation uncertainties, we jointly and dynamically optimize VTs' construction and PTs' task offloading, along with communication and computation resource allocations. Observing that decision variables are asynchronous with different triggers, we propose a novel two-timescale accuracy-aware online optimization approach (TACO). Specifically, TACO utilizes an improved Lyapunov method to decompose the problem into multiple instant ones, and then leverages piecewise McCormick envelopes and block coordinate descent based algorithms, addressing two timescales alternately. Theoretical analyses and simulations show that the proposed approach can reach asymptotic optimum within a polynomial-time complexity, and demonstrate its superiority over counterparts.

翻译：人体数字孪生（HDT）是一种新兴范式，通过连接物理孪生（PTs）与强大的虚拟孪生（VTs），辅助以人为中心的复杂任务执行。本文研究端-边-云协同框架下构建HDT的双时间尺度在线优化问题。作为HDT的独特特性，我们考虑将PTs对应的VTs部署在边缘服务器上，其构成不仅包括通过从云端下载经验知识而部署的通用模型，还包括通过从终端设备采集个性化数据而更新的定制化模型。为在严格的能量与延迟约束下最大化任务执行精度，并兼顾HDT固有的移动性与状态变化不确定性，我们联合且动态地优化VTs的构建、PTs的任务卸载，以及通信与计算资源的分配。鉴于决策变量具有不同的触发时机且异步运行，我们提出一种新颖的双时间尺度精度感知在线优化方法（TACO）。具体而言，TACO利用改进的Lyapunov方法将原问题分解为多个即时子问题，进而借助分段McCormick包络与基于块坐标下降的算法，交替处理两个时间尺度的问题。理论分析与仿真结果表明，所提方法可在多项式时间复杂度内渐近逼近最优解，并证明了其相较于现有方法的优越性。