Path planning for robotic exploration is challenging, requiring reasoning over unknown spaces and anticipating future observations. Efficient exploration requires selecting budget-constrained paths that maximize information gain. Despite advances in autonomous exploration, existing algorithms still fall short of human performance, particularly in structured environments where predictive cues exist but are underutilized. Guided by insights from our user study, we introduce MapExRL, which improves robot exploration efficiency in structured indoor environments by enabling longer-horizon planning through a learned policy and global map predictions. Unlike many learning-based exploration methods that use motion primitives as the action space, our approach leverages frontiers for more efficient model learning and longer horizon reasoning. Our framework generates global map predictions from the observed map, which our policy utilizes, along with the prediction uncertainty, estimated sensor coverage, frontier distance, and remaining distance budget, to assess the strategic long-term value of frontiers. By leveraging multiple frontier scoring methods and additional context, our policy makes more informed decisions at each stage of the exploration. We evaluate our framework on a real-world indoor map dataset, achieving up to an 18.8% improvement over the strongest state-of-the-art baseline, with even greater gains compared to conventional frontier-based algorithms. Website: https://mapexrl.github.io