# Should I update action value functions when there is no change?

Suppose there is a website and the decision-maker wants to recommend some products to each customer visiting the website. Customers visit the websites in which the time interval between two consecutive visits is a random variable (in some cases it might take one time unit, in some cases it might take several time units, like the concepts in SMDP). When a customer visits the website but there is no purchase, there would be no reward. Should I update the $$Q$$ function even when there is no reward? In this situation, I should set $$R_{t+1}=0$$ and use any updating method like Q-learning? Moreover, if I consider eligibility trace and $$\tau$$ represents the time units between two-arrival, should I update eligibility trace like $$E(s,a)=\gamma^\tau \lambda E(s,a)+1$$?

Thanks