Contextual A/B Testing With Martingale In Online Learning

When two schemes(such as two pages)are formulated for the same goal,the twoversion(A/B)testing process can collect the experience data and business data of the two groups of users,analyze and evaluate the better version.As an effective business strategy,A/B testing has a wide range of applications in the industry,such as the comparison of new products(or services)and old products(or services)in traditional industries or Internet technologies,and the comparison of different drugs in the pharmaceutical industry,etc.Therefore,A/B testing is becoming a research hotspot in the field of management science and engineering,which can provide decision support for the refined operation of enterprise organizations.However,the lack of overlap between the characteristic information of the two groups of observed entities in the collected data makes it difficult to effectively identify and compare in A/B test.Bayesian A/B test uses prior information to obtain two sets of data and compare the conversion rates of the two groups;although this process improves the interpretability of the test results,it does not consider the characteristic information of the sample itself.In view of this,this paper constructs the online learning model of contextual A/B testing based on martingale.The main contents are summarized as follows:Firstly,a contextual A/B test model based on user characteristic information was built to eliminate the adverse effects of user characteristic information on the traditional A/B test model.The covariate space was constructed by sample feature information,and the nearest neighbor algorithm of propensity score matching was used to match the samples.The matched data set was used as the input of the Bayesian A/B test model to calculate the posterior expected loss probability.Compared with the traditional A/B testing model,the contextual A/B testing model proposed in this paper has higher test accuracy and stronger interpretability of test results.Numerical experiments demonstrate the effectiveness of this method compared to traditional methods.Secondly,the martingale stopping time and martingale convergence theory of the parameters with the A/B test model was proposed,which theoretically guarantees the effectiveness of the proposed A/B test model.The theory defined the martingale stopping time rule,convergence expectation,and convergence boundary of the A/B test parameters,and constructed the corresponding solution steps and algorithms.Through the conditional expectation equation,the optimal parameters estimated by the algorithm are obtained.Thirdly,A/B testing model was extended to the online learning process.The improved online learning model based on A/B testing is suitable for more scenarios.The potential errors that may occur during product testing experiments and the strategies to avoid these errors are determined,making the online testing technology more practical.Finally,using the diabetes case data set and online medical data set to further verify the effectiveness of the model.