We address the challenge of finding algorithms for online allocation (i.e. bipartite matching) using a machine learning approach. In this paper, we focus on the AdWords problem, which is a classical online budgeted matching problem of both theoretical and practical significance. In contrast to existing work, our goal is to accomplish algorithm design {\em tabula rasa}, i.e., without any human-provided insights or expert-tuned training data beyond specifying the objective and constraints of the optimization problem. We construct a framework based on insights from game theory and adversarial training. Key to our approach is to generate adversarial examples that expose the weakness of any given algorithm. A unique challenge in our context is to generate complete examples from scratch rather than perturbing given examples and we demonstrate this can be accomplished for the Adwords problem. We use this framework to co-train an algorithm network and an adversarial network against each other until they converge to an equilibrium. This approach finds algorithms and adversarial examples that are consistent with known optimal results. Secondly, we address the question of robustness of the algorithm, namely can we design algorithms that are both strong under practical distributions, as well as exhibit robust performance against adversarial instances. To accomplish this, we train algorithm networks using a mixture of adversarial and fixed practical distributions like power-laws; the resulting networks exhibit a smooth trade-off between the two input regimes.