  We study Markov decision processes (MDPs), where agents have direct control
over when and how they gather information, as formalized by action-contingent
noiselessly observable MDPs (ACNO-MPDs). In these models, actions consist of
two components: a control action that affects the environment, and a
measurement action that affects what the agent can observe. To solve ACNO-MDPs,
we introduce the act-then-measure (ATM) heuristic, which assumes that we can
ignore future state uncertainty when choosing control actions. We show how
following this heuristic may lead to shorter policy computation times and prove
a bound on the performance loss incurred by the heuristic. To decide whether or
not to take a measurement action, we introduce the concept of measuring value.
We develop a reinforcement learning algorithm based on the ATM heuristic, using
a Dyna-Q variant adapted for partially observable domains, and showcase its
superior performance compared to prior methods on a number of
partially-observable environments.
