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An important goal in reinforcement learning is to create agents that can quickly adapt to new goals while avoiding situations that might cause damage to themselves or their environments. One way agents learn is through exploration mechanisms, which are needed to discover new policies. However, in deep reinforcement learning, exploration is normally done by injecting noise in the action space. While performing well in many domains, this setup has the inherent risk that the noisy actions performed by the agent lead to unsafe states in the environment. Here we introduce a novel approach called Meta-Learned Instinctual Networks (MLIN) that allows agents to safely learn during their lifetime while avoiding potentially hazardous states. At the core of the approach is a plastic network trained through reinforcement learning and an evolved "instinctual" network, which does not change during the agent's lifetime but can modulate the noisy output of the plastic network. We test our idea on a simple 2D navigation task with no-go zones, in which the agent has to learn to approach new targets during deployment. MLIN outperforms standard meta-trained networks and allows agents to learn to navigate to new targets without colliding with any of the no-go zones. These results suggest that meta-learning augmented with an instinctual network is a promising new approach for safe AI, which may enable progress in this area on a variety of different domains.