Rate-Distortion Theoretic Bounds on Generalization Error for Distributed Learning
This provides theoretical guarantees for distributed machine learning systems, which is incremental as it extends existing rate-distortion approaches to distributed scenarios.
The paper tackles the problem of bounding generalization error in distributed learning by using rate-distortion theory, resulting in tighter bounds that show generalization error decays faster in distributed settings, such as with a factor of O(log(K)/√K) for distributed SVMs.
In this paper, we use tools from rate-distortion theory to establish new upper bounds on the generalization error of statistical distributed learning algorithms. Specifically, there are $K$ clients whose individually chosen models are aggregated by a central server. The bounds depend on the compressibility of each client's algorithm while keeping other clients' algorithms un-compressed, and leverage the fact that small changes in each local model change the aggregated model by a factor of only $1/K$. Adopting a recently proposed approach by Sefidgaran et al., and extending it suitably to the distributed setting, this enables smaller rate-distortion terms which are shown to translate into tighter generalization bounds. The bounds are then applied to the distributed support vector machines (SVM), suggesting that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of $\mathcal{O}(\log(K)/\sqrt{K})$. This finding is validated also experimentally. A similar conclusion is obtained for a multiple-round federated learning setup where each client uses stochastic gradient Langevin dynamics (SGLD).