Efficient exploration of design spaces is highly sought after in engineering applications. A spectrum of tools has been proposed to deal with the computational difficulties associated with such problems. In the context of our case study, these tools can be broadly classified into optimization and supervised learning approaches. Optimization approaches, while successful, are inherently data inefficient, with evolutionary optimization-based methods being a good example. This inefficiency stems from data not being reused from previous design explorations. Alternately, supervised learning-based design paradigms are data efficient. However, the quality of ensuing solutions depends heavily on the quality of data available. Furthermore, it is difficult to incorporate physics models and domain knowledge aspects of design exploration into pure-learning-based methods. In this work, we formulate a reinforcement learning (RL)-based design framework that mitigates disadvantages of both approaches. Our framework simultaneously finds solutions that are more efficient compared with supervised learning approaches while using data more efficiently compared with genetic algorithm (GA)-based optimization approaches. We illustrate our framework on a problem of microfluidic device design for flow sculpting, and our results show that a single generic RL agent is capable of exploring the solution space to achieve multiple design objectives. Additionally, we demonstrate that the RL agent can be used to solve more complex problems using a targeted refinement step. Thus, we address the data efficiency limitation of optimization-based methods and the limited data problem of supervised learning-based methods. The versatility of our framework is illustrated by utilizing it to gain domain insights and to incorporate domain knowledge. We envision such RL frameworks to have an impact on design science.