Most multi-robot task allocation methods rely on communication to resolve conflicts and reach consistent assignments. In environments with limited bandwidth, degraded infrastructure, or adversarial interference, existing approaches degrade sharply. We introduce a learning-based framework that achieves high-quality task allocation without any robot-to-robot communication. The key idea is that robots coordinate implicitly by predicting teammates’ bids. While analytical predictions assume idealized conditions (uniform distributions, known bid functions), our learned approach adapts to task clustering and spatial heterogeneity. We train bid predictors end-to-end to minimize Task Allocation Regret rather than prediction error. To scale to large swarms, we develop a mean-field approximation, reducing complexity from O(NT) to O(T). We call our approach FORMICA: Field-Oriented Regret-Minimizing Implicit Coordination Algorithm. Experiments show FORMICA substantially outperforms a natural analytical baseline. Training requires only 21 s on a laptop, enabling rapid adaptation to new environments.