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Multi-agent foraging (MAF) involves distributing a team of agents to search an environment and extract resources from it. Nature provides several examples of highly effective foragers, where individuals within the foraging collective use biological markers (e.g., pheromones) to communicate critical information to others via the environment. In this work, we propose ForMIC, a distributed reinforcement learning MAF approach that endows agents with implicit communication abilities via their shared environment. However, learning efficient policies with stigmergic interactions is highly nontrivial, since agents need to perform well to send each other useful signals, but also need to sense others' signals to perform well. In this work, we develop several key learning techniques for training policies with stigmergic interactions, where such a circular dependency is present. By relying on clever curriculum learning design, action filtering, and the introduction of non-learning agents to increase the agent density at training time at low computational cost, we develop a minimal learning framework that leads to the stable training of efficient stigmergic policies. We present simulation results which demonstrate that our learned policy outperforms existing state-of-the-art MAF algorithms in a set of experiments that vary team size, number and placement of resources, and key environmental dynamics not seen at training time.