- Abstract: We tackle the challenge of using machine learning to find algorithms with strong worst-case guarantees for online combinatorial optimization problems. Whereas the previous approach along this direction (Kong et al., 2018) relies on significant domain expertise to provide hard distributions over input instances at training, we ask whether this can be accomplished from first principles, i.e., without any human-provided data beyond specifying the objective of the optimization problem. To answer this question, we draw insights from classic results in game theory, analysis of algorithms, and online learning to introduce a novel framework. At the high level, similar to a generative adversarial network (GAN), our framework has two components whose respective goals are to learn the optimal algorithm as well as a set of input instances that captures the essential difficulty of the given optimization problem. The two components are trained against each other and evolved simultaneously. We test our ideas on the ski rental problem and the fractional AdWords problem. For these well-studied problems, our preliminary results demonstrate that the framework is capable of finding algorithms as well as difficult input instances that are consistent with known optimal results. We believe our new framework points to a promising direction which can facilitate the research of algorithm design by leveraging ML to improve the state of the art both in theory and in practice.