This paper proposes a theoretical framework to evaluate and compare the performance of gradient-descent algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have noticed that convergence toward flat local minima tend to enhance the generalization ability of learning algorithms. This work discovers two interesting results. First, it shows that decentralized learning strategies are able to escape faster away from local minimizers and favor convergence toward flatter minima relative to the centralized solution in the large-batch training regime. Second, and importantly, the ultimate classification accuracy is not solely dependent on the flatness of the local minimizer but also on how well a learning algorithm can approach that minimum. In other words, the classification accuracy is a function of both flatness and optimization performance. The paper examines the interplay between the two measures of flatness and optimization error closely. One important conclusion is that decentralized strategies of the diffusion type deliver enhanced classification accuracy because it strikes a more favorable balance between flatness and optimization performance.

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