Research On Generalization Of Multi-task Learning Models

At present,social production is inseparable from machine learning,which has provided great convenience to our lives and also provided an impetus for the development of social productivity.Multi-task learning is an important branch that can improve training efficiency,reduce sample requirements,and be successfully applied in many aspects.However,the existing generalization bounds for multi-task learning are mostly referred to as the upper bounds of the probability that the sum of generalization gaps of multiple tasks is larger than some positive constant,leading to the consequence that the performance of each task cannot be evaluated individually.Therefore,it is still not clear how the tasks affect the generalization of multi-task learning.To overcome this problem,this paper studies the consistency,effectiveness,and generalization of multi-task learning by regarding multi-task learning as vector-valued functions learning and with the help of the task-group relatedness matrix.Specifically,this paper derives symmetric inequalities and deviation inequalities applicable to vector-valued functions and extends the covering number of scalar-valued function classes to vector-valued function classes.This paper also proposes the task-group relatedness matrix to study the impact of tasks on the performance of multi-task learning.Finally,using the above basic tools,this paper gives estimates of the generalization bounds of multi-task learning in two different meanings.Based on the results obtained,this paper analyzes several theoretical issues of multi-task learning,including model performance,sample requirements,consistency of each task,model validity,and so on,comparing with single-task learning.Another use of the task-group relatedness matrix is to empirically measure whether the model can accurately use the task relatedness of the current task group to improve its performance.To this end,this paper presents a method of empirically computing the task-group relatedness matrix,and based on the obtained theoretical results,two schemes that can help test or improve the performance of multi-task learning models are proposed.The results of numerical experiments prove the feasibility and effectiveness of the schemes.