We study sequential experiments where sampling is costly and a decision-maker aims to determine the best treatment for full-scale implementation by (1) adaptively allocating units between two possible treatments, and (2) stopping the experiment when the expected welfare (inclusive of sampling costs) from implementing the chosen treatment is maximised. Working under a continuous time limit, we characterise the optimal policies under the minimax regret criterion. We show that the same policies also remain optimal under both parametric and non-parametric outcome distributions in an asymptotic regime where sampling costs approach zero. The minimax optimal sampling rule is just the Neyman allocation: it is independent of sampling costs and does not adapt to observed outcomes. The decision-maker halts sampling when the product of the average treatment difference and the number of observations surpasses a specific threshold. The results derived also apply to the so-called best-arm identification problem, where the number of observations is exogenously specified.

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to estimate various terms in the pseudo-log-likelihood function. We suggest two approaches: The first—linear semi-gradient—provides approximations to the recursive terms using basis functions. The second—Approximate Value Iteration—builds a sequence of approximations to the recursive terms by solving non-parametric estimation problems. Our approaches are fast and naturally allow for continuous and/or high-dimensional state spaces. Furthermore, they do not require specification of transition densities. In dynamic games, they avoid integrating over other players’ actions, further heightening the computational advantage. Our proposals can be paired with popular existing methods such as pseudo-maximum-likelihood, and we propose locally robust corrections for the latter to achieve parametric rates of convergence. Monte Carlo simulations confirm the properties of our algorithms in practice.