Linear Speedup in Personalized Collaborative Learning
This work addresses the challenge of improving model accuracy for individual users in collaborative settings by balancing bias and variance, offering theoretical and empirical insights for incremental advancements in personalized machine learning.
The paper tackles the problem of personalized collaborative learning by formalizing it as stochastic optimization with one main task and N auxiliary tasks, providing convergence guarantees for weighted gradient averaging and a novel bias correction method, and showing conditions for linear speedup with respect to N, supported by empirical validation.
Collaborative training can improve the accuracy of a model for a user by trading off the model's bias (introduced by using data from other users who are potentially different) against its variance (due to the limited amount of data on any single user). In this work, we formalize the personalized collaborative learning problem as a stochastic optimization of a task 0 while giving access to N related but different tasks 1,..., N. We provide convergence guarantees for two algorithms in this setting -- a popular collaboration method known as weighted gradient averaging, and a novel bias correction method -- and explore conditions under which we can achieve linear speedup w.r.t. the number of auxiliary tasks N. Further, we also empirically study their performance confirming our theoretical insights.