  Online algorithm is an important branch in algorithm design. Designing online
algorithms with a bounded competitive ratio (in terms of worst-case
performance) can be hard and usually relies on problem-specific assumptions.
Inspired by adversarial training from Generative Adversarial Net (GAN) and the
fact that competitive ratio of an online algorithm is based on worst-case
input, we adopt deep neural networks to learn an online algorithm for a
resource allocation and pricing problem from scratch, with the goal that the
performance gap between offline optimum and the learned online algorithm can be
minimized for worst-case input.
  Specifically, we leverage two neural networks as algorithm and adversary
respectively and let them play a zero sum game, with the adversary being
responsible for generating worst-case input while the algorithm learns the best
strategy based on the input provided by the adversary. To ensure better
convergence of the algorithm network (to the desired online algorithm), we
propose a novel per-round update method to handle sequential decision making to
break complex dependency among different rounds so that update can be done for
every possible action, instead of only sampled actions. To the best of our
knowledge, our work is the first using deep neural networks to design an online
algorithm from the perspective of worst-case performance guarantee. Empirical
studies show that our updating methods ensure convergence to Nash equilibrium
and the learned algorithm outperforms state-of-the-art online algorithms under
various settings.
