The tidal waves of modern electronic/electrical devices have led to increasing demands for ubiquitous application-specific power converters. A conventional manual design procedure of such power converters is computation- and labor-intensive, which involves selecting and connecting component devices, tuning component-wise parameters and control schemes, and iteratively evaluating and optimizing the design. To automate and speed up this design process, we propose an automatic framework that designs custom power converters from design specifications using reinforcement learning. Specifically, the framework embraces upper-confidence-bound-tree-based (UCT-based) reinforcement learning to automate topology space exploration with circuit design specification-encoded reward signals. Moreover, our UCT-based approach can exploit small offline data via the specially designed default policy to accelerate topology space exploration. Further, it utilizes a hybrid circuit evaluation strategy to substantially reduces design evaluation costs. Empirically, we demonstrated that our framework could generate energy-efficient circuit topologies for various target voltage conversion ratios. Compared to existing automatic topology optimization strategies, the proposed method is much more computationally efficient — it can generate topologies with the same quality while being up to 67% faster. Additionally, we discussed some interesting circuits discovered by our framework.