Split learning recently emerged as a solution for distributed machine learning with heterogeneous IoT devices, where clients can offload part of their training to computationally-powerful helpers. The core challenge in split learning is to minimize the training time by jointly devising the client-helper assignment and the schedule of tasks at the helpers. We first study the model where each helper has a memory cardinality constraint on how many clients it may be assigned, which represents the case of homogeneous tasks. Through complexity theory, we rule out exact polynomial-time algorithms and approximation schemes even for highly restricted instances of this problem. We complement these negative results with a non-trivial polynomial-time 5-approximation algorithm. Building on this, we then focus on the more general heterogeneous task setting considered by Tirana et al. [INFOCOM 2024], where helpers have memory capacity constraints and clients have variable memory costs. In this case, we prove that, unless P=NP, the problem cannot admit a polynomial-time approximation algorithm for any approximation factor. However, by adapting our aforementioned 5-approximation algorithm, we develop a novel heuristic for the heterogeneous task setting and show that it outperforms heuristics from prior works through extensive experiments.

翻译：拆分学习最近作为一种面向异构物联网设备的分布式机器学习解决方案出现，其中客户端可以将部分训练任务卸载给计算能力强大的辅助节点。拆分学习的核心挑战在于通过联合设计客户端-辅助节点分配方案以及辅助节点上的任务调度，以最小化训练时间。我们首先研究每个辅助节点存在内存基数约束（即其可分配的客户端数量上限）的模型，这代表了同构任务的情形。通过复杂性理论，我们排除了针对该问题高度受限实例的精确多项式时间算法和近似方案存在的可能性。我们通过一个非平凡的多项式时间5-近似算法对这些否定性结论进行了补充。在此基础上，我们进一步关注Tirana等人[INFOCOM 2024]考虑的更具一般性的异构任务场景，其中辅助节点具有内存容量约束，而客户端具有可变的内存开销。在此情况下，我们证明除非P=NP，否则该问题对于任意近似比都不存在多项式时间近似算法。然而，通过改进我们前述的5-近似算法，我们为异构任务场景提出了一种新颖的启发式方法，并通过大量实验证明其性能优于现有工作中的启发式方法。