Temporal Correlations and Optimal Feedback Control of an Active Information Engine

How much does a feedback controller need to know about the fluctuations it exploits? We address this question using a macroscopic information engine driven by self-propelled bristle-robots. Experimentally measured occupancy time series show that temporal correlations strongly affect vacancy detection. At short measurement intervals, mean first-passage times exceed independent-measurement predictions by more than an order of magnitude. A first-order Markov approximation captures much of this effect. It does not reproduce the full first-passage distribution, revealing higher-order temporal memory. Nevertheless, Markov-selected protocols come within 0.15\% of the maximum experimental power. Neglecting correlations causes power losses of several percent and favors larger compression distances. Introducing a sensing cost shifts the optimal strategy toward sparse sensing. The independent model cannot predict this shift, whereas the Markov model captures it. Cross-validation on separate time segments confirms the near-optimal performance of Markov-selected protocols. These findings demonstrate that near-optimal feedback control in correlated nonequilibrium systems can require a simpler statistical description than predicting their full temporal dynamics.