Over the past few years, Reinforcement Learning combined with Deep Learning techniques has successfully proven to solve complex problems in various domains including robotics, self-driving cars, finance, and gaming. In this paper, we are introducing Reinforcement Learning (RL) to another domain - visualization. Our novel point-feature label placement method utilizes Multi-Agent Deep Reinforcement Learning (MADRL) to learn label placement strategy, which is the first machine-learning-driven labeling method in contrast to existing hand-crafted algorithms designed by human experts. To facilitate the RL learning paradigm, we developed an environment where an agent acts as a proxy for a label, a short textual annotation that augments visualizations like geographical maps, illustrations, and technical drawings. Our results demonstrate that the strategy trained by our method significantly outperforms the random strategy of an untrained agent and also performs superior to the compared methods designed by human experts in terms of completeness (i.e., the number of placed labels). The trade-off is increased computation time, making the proposed method slower than compared methods. Nevertheless, our method is ideal for situations where the labeling can be computed in advance, and completeness is essential, such as cartographic maps, technical drawings, and medical atlases. Additionally, we conducted a user study to assess the perceived performance. The outcomes revealed that the participants considered the proposed method to be significantly better than the other examined methods. This indicates that the improved completeness is not just reflected in the quantitative metrics but also in the subjective evaluation of the participants.