The use of adaptive design and surrogate endpoint have become increasingly popular in clinical research. Adaptive design allows for modifications to the trial as more data is accrued, allowing for flexibility and efficiency. Surrogate endpoints circumvent issues that arise when the primary endpoint of interest proves difficult to assay. We study the use of an optimal surrogate in the context of a targeted, adaptive, sequential design that aims to learn several target parameters- including the optimal dynamic rule and its mean reward. We define the optimal surrogate for the first round of sequential randomization as the function of the data generating distribution collected by the intermediate time point that satisfies the Prentice definition. We describe several ways of defining an optimal surrogate, with modifications to the randomization scheme dependent on the surrogate. Finally, we show that we can obtain valid inference for the target parameter(s) without collecting the long-term final outcome, while taking into account the uncertainty in the estimator of the optimal surrogate. As such, we allow for adaptive designs in settings where collecting long-term outcome is infeasible.