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Building an AI agent that can design on its own has been a goal since the 1980s. Recently, deep learning has shown the ability to learn from large-scale data, enabling significant advances in data-driven design. However, learning over prior data limits us only to solve problems that have been solved before and biases data-driven learning towards existing solutions. The ultimate goal for a design agent is the ability to learn generalizable design behavior in a problem space without having seen it before. We introduce a self-learning agent framework in this work that achieves this goal. This framework integrates a deep policy network with a novel tree search algorithm, where the tree search explores the problem space, and the deep policy network leverages self-generated experience to guide the search further. This framework first demonstrates an ability to discover high-performing generative strategies without any prior data, and second, it illustrates a zero-shot generalization of generative strategies across various unseen boundary conditions. This work evaluates the effectiveness and versatility of the framework by solving multiple versions of two engineering design problems without retraining. Overall, this paper presents a methodology to self-learn high-performing and generalizable problem-solving behavior in an arbitrary problem space, circumventing the needs for expert data, existing solutions, and problem-specific learning.