  Many reinforcement learning algorithms are built on an assumption that an
agent interacts with an environment over fixed-duration, discrete time steps.
However, physical systems are continuous in time, requiring a choice of
time-discretization granularity when digitally controlling them. Furthermore,
such systems do not wait for decisions to be made before advancing the
environment state, necessitating the study of how the choice of discretization
may affect a reinforcement learning algorithm. In this work, we consider the
relationship between the definitions of the continuous-time and discrete-time
returns. Specifically, we acknowledge an idiosyncrasy with naively applying a
discrete-time algorithm to a discretized continuous-time environment, and note
how a simple modification can better align the return definitions. This
observation is of practical consideration when dealing with environments where
time-discretization granularity is a choice, or situations where such
granularity is inherently stochastic.
