  The difficulty of optimal control problems has classically been characterized
in terms of system properties such as minimum eigenvalues of
controllability/observability gramians. We revisit these characterizations in
the context of the increasing popularity of data-driven techniques like
reinforcement learning (RL), and in control settings where input observations
are high-dimensional images and transition dynamics are unknown. Specifically,
we ask: to what extent are quantifiable control and perceptual difficulty
metrics of a task predictive of the performance and sample complexity of
data-driven controllers? We modulate two different types of partial
observability in a cartpole "stick-balancing" problem -- (i) the height of one
visible fixation point on the cartpole, which can be used to tune fundamental
limits of performance achievable by any controller, and by (ii) the level of
perception noise in the fixation point position inferred from depth or RGB
images of the cartpole. In these settings, we empirically study two popular
families of controllers: RL and system identification-based $H_\infty$ control,
using visually estimated system state. Our results show that the fundamental
limits of robust control have corresponding implications for the
sample-efficiency and performance of learned perception-based controllers.
Visit our project website https://jxu.ai/rl-vs-control-web for more
information.
