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

How Are Learned Perception-Based Controllers Impacted by the Limits of Robust Control?