  Finite-horizon sequential experimental design (SED) arises naturally in many
contexts, including hyperparameter tuning in machine learning among more
traditional settings. Computing the optimal policy for such problems requires
solving Bellman equations, which are generally intractable. Most existing work
resorts to severely myopic approximations by limiting the decision horizon to
only a single time-step, which can underweight exploration in favor of
exploitation. We present BINOCULARS: Batch-Informed NOnmyopic Choices, Using
Long-horizons for Adaptive, Rapid SED, a general framework for deriving
efficient, nonmyopic approximations to the optimal experimental policy. Our key
idea is simple and surprisingly effective: we first compute a one-step optimal
batch of experiments, then select a single point from this batch to evaluate.
We realize BINOCULARS for Bayesian optimization and Bayesian quadrature -- two
notable SED problems with radically different objectives -- and demonstrate
that BINOCULARS significantly outperforms myopic alternatives in real-world
scenarios.
