  There are notable examples of online search improving over hand-coded or
learned policies (e.g. AlphaZero) for sequential decision making. It is not
clear, however, whether or not policy improvement is guaranteed for many of
these approaches, even when given a perfect evaluation function and transition
model. Indeed, simple counter examples show that seemingly reasonable online
search procedures can hurt performance compared to the original policy. To
address this issue, we introduce the choice function framework for analyzing
online search procedures for policy improvement. A choice function specifies
the actions to be considered at every node of a search tree, with all other
actions being pruned. Our main contribution is to give sufficient conditions
for stationary and non-stationary choice functions to guarantee that the value
achieved by online search is no worse than the original policy. In addition, we
describe a general parametric class of choice functions that satisfy those
conditions and present an illustrative use case of the framework's empirical
utility.
