A sequential procedure for estimating the difference of two normal means when the variances are unknown and not necessarily equal is proposed, and an asymptotic expression for "regret" is given. This generalizes the corresponding one sample result of Woodroofe.
"Sequential Point Estimation of the Difference of Two Normal Means." Ann. Statist. 8 (1) 221 - 225, January, 1980. https://doi.org/10.1214/aos/1176344906