Homing through Reinforcement Learning
Homing and navigation are fundamental behaviors in biological systems that enable agents to reliably reach a target under uncertainty. We present a Reinforcement Learning (RL) framework to model adaptive homing in continuous two-dimensional domain. In this framework, the agent's state is given by its angular deviation from home, actions correspond to alignment or stochastic reorientation, and learning is driven by a radial-distance-based cost that penalizes motion away from the target, where the cost also acts as an effective signal guiding the agent towards the home. For a single self-propelled agent moving with constant speed, we find that the mean homing time $\langle T_{\mathrm{home}} \rangle$ exhibits a non-monotonic dependence on the rotational diffusion strength $D_r$, with an optimal noise level $D_r^\ast$, revealing a subtle interplay between exploration and goal-directed correction. Extending to two agents with soft repulsion, one agent consistently reaches home faster than the other, while in multi-agents system, repulsion ensures separation and the fastest agent becomes progressively faster as group size increases. Finally, we have compared the homing time obtained from the RL agent with that of an Active Brownian Particle (ABP) with resetting and a pure ABP (without resetting) under identical conditions. The RL-based agent consistently achieves shorter homing times with trajectories that are less noisy and more directed than both cases, while the pure ABP typically continues wandering near the target without reliable localization. Our results show that cost-driven learning, stochastic reorientation, and inter-agent interactions enable efficient adaptive navigation, linking individual and collective homing. This RL framework captures key biological features such as feedback-based route learning, randomness to escape unfavorable orientations, and mutual coordination.