  Coded distributed computing framework enables large-scale machine learning
(ML) models to be trained efficiently in a distributed manner, while mitigating
the straggler effect. In this work, we consider a multi-task assignment problem
in a coded distributed computing system, where multiple masters, each with a
different matrix multiplication task, assign computation tasks to workers with
heterogeneous computing capabilities. Both dedicated and probabilistic worker
assignment models are considered, with the objective of minimizing the average
completion time of all computations. For dedicated worker assignment, greedy
algorithms are proposed and the corresponding optimal load allocation is
derived based on the Lagrange multiplier method. For probabilistic assignment,
successive convex approximation method is used to solve the non-convex
optimization problem. Simulation results show that the proposed algorithms
reduce the completion time by 80% over uncoded scheme, and 49% over an
unbalanced coded scheme.
