On the Asymptotic Bias of the Diffusion-Based Distributed Pareto Optimization

We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the bias of this algorithm at small step-sizes and show that the bias descends to zero with a linear dependence on the largest step-size parameter when this parameter is sufficiently small. Our methodology provides new insights into the inner workings of diffusion Pareto optimization algorithm while being considerably simpler than the small-step-size asymptotic bias analysis presented in the original work that introduced the algorithm. This is because we take advantage of the special eigenstructure of the composite combination matrix used in the algorithm without calling for any eigenspace decomposition or matrix inversion.