We discuss a super-learning of an optimal individualized treatment rule based on observing a sample of n individuals over time, and a CV-TMLE of its mean outcome with inference. We then present sequential adaptive designs involving enrolling individuals over time, and setting the randomization probabilities in response to the observed data on previously enrolled subjects. In particular, we demonstrate the utility of surrogates to make such designs able to use data on subjects that have not reached their endpoint yet. We present online super-learner of optimal rule based on past data, a method for determining the randomization probabilities robustly, and a TMLE for the mean outcome under the learned optimal rule. Finally, we present online adaptive designs and corresponding estimators of the optimal rule and its mean outcome based on observing a unit specific single time series, or multiple time series across individuals, allowing for asymptotic inference in the number of time points. Methods are demonstrated with simulated data and real data.