Phase diagram of optimal strategies with mixed directional and non-directional sensing

Determine the phase diagram of optimal navigation strategies that maximize mean up-gradient speed in the information-limited framework when an agent has a bilateral pair of sensors providing two concurrent cues: (i) a noisy directional signal given by the difference of the two sensor readings and (ii) a less noisy non-directional signal given by their sum. Characterize which strategies (e.g., continuous steering toward the gradient, run-and-tumble reorientation, reversing, right-angle flicks, or discrete-angle turn policies) are optimal as functions of the relative information rates or noise levels of the directional and non-directional channels, and identify the transitions between these regimes.

Background

The paper establishes that, under information constraints, continuous steering is optimal when full directional information about heading relative to the gradient is available, whereas discrete reorientation strategies (e.g., reversing, tumbling, flicks, or discrete-angle turns) are optimal when only non-directional, scalar information is available. It further shows transitions between these discrete strategies as the allowed information rate varies.

In realistic sensing scenarios, such as bilateral sensors, a directional cue (difference between left and right sensors) and a non-directional cue (sum of sensor readings) coexist but with different noise properties, implying different attainable information rates. The authors note that comparing strategies across channels of unequal informational cost complicates the optimization, and they explicitly state that the overall phase diagram of optimal behaviors in this mixed-cue setting is unknown.

Resolving this would extend the current results by mapping the regions in parameter space (e.g., directional vs non-directional information rates or signal-to-noise ratios) where different strategies maximize up-gradient speed, and identifying the boundaries separating continuous-steering regimes from discrete-turn regimes and among various discrete-turn policies.