Abstract
The explore/exploit trade-off is the core problem of reinforcement learning (RL). We show that a minimal foraging swarm approaches its optimum - the ideal-free / Nash allocation of a multi-agent resource-sharing game (an equilibrium, not a return maximum) - with no learner and no reward signal. Agents explore by heavy-tailed (Levy) flights, recruit neighbours to a discovery through a threshold cascade on their proximity network, and disperse as a patch crowds; this cascade cycle balances exploration and exploitation and drives foragers toward the ideal free distribution. The swarm attains the shape of this optimum (committed foragers track richness with slope 0.94) but not its exact equilibrium - it stays measurably exploitable - reaching it dynamically (~150 steps) through the coupling of recruitment to movement: remove the coupling and matching collapses (0.94 -> 0.08). The RL sits at the level of the problem and the allocation reached, not the micro-rule: no step evaluates payoff (reward-free by construction, though the crowd signal is informationally tied to payoff), and the swarm reaches the allocation without learning it (quality plateaus and re-settles after resources move, no cumulative gain). Against a trained baseline the comparison is two-sided: in an easier, disembodied game a learner is more precise, while in the same embodied environment the reward-free swarm reaches ~65% of a validated oracle ceiling at zero training and leads until trained PPO and centralised-critic (CTDE) learners overtake it (~74-75%, 16 seeds, all above the swarm mean) after ~4,000 of 15,000 training steps - its advantage is in budget, not asymptote. In this one setting we read it not as beating RL but as a strong zero-shot, reward-free operating point: a demonstration that the self-organizing physics of a minimal swarm can carry a collective close to the optimum RL seeks, with none of RL's machinery.
Abstract (translated)
URL
https://arxiv.org/abs/2610.25113
