@article{Wilder_2018, title={Equilibrium Computation and Robust Optimization in Zero Sum Games With Submodular Structure}, volume={32}, url={https://ojs.aaai.org/index.php/AAAI/article/view/11455}, DOI={10.1609/aaai.v32i1.11455}, abstractNote={ <p> We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem of robustly optimizing a submodular function over the worst case from a set of scenarios. The challenge in computing equilibria is that both players’ strategy spaces can be exponentially large. Accordingly, previous algorithms have worst-case exponential runtime and indeed fail to scale up on practical instances. We provide a pseudopolynomial-time algorithm which obtains a guaranteed (1 - 1/e)^2-approximate mixed strategy for the maximizing player. Our algorithm only requires access to a weakened version of a best response oracle for the minimizing player which runs in polynomial time. Experimental results for network security games and a robust budget allocation problem confirm that our algorithm delivers near-optimal solutions and scales to much larger instances than was previously possible. </p> }, number={1}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Wilder, Bryan}, year={2018}, month={Apr.} }