  A default assumption in reinforcement learning (RL) and optimal control is
that observations arrive at discrete time points on a fixed clock cycle. Yet,
many applications involve continuous-time systems where the time
discretization, in principle, can be managed. The impact of time discretization
on RL methods has not been fully characterized in existing theory, but a more
detailed analysis of its effect could reveal opportunities for improving
data-efficiency. We address this gap by analyzing Monte-Carlo policy evaluation
for LQR systems and uncover a fundamental trade-off between approximation and
statistical error in value estimation. Importantly, these two errors behave
differently to time discretization, leading to an optimal choice of temporal
resolution for a given data budget. These findings show that managing the
temporal resolution can provably improve policy evaluation efficiency in LQR
systems with finite data. Empirically, we demonstrate the trade-off in
numerical simulations of LQR instances and standard RL benchmarks for
non-linear continuous control.
