Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to improve solution quality due to non-smoothness issues that arise when training through a complex optimization layer. To address these shortcomings, we learn a low-dimensional surrogate model of a large optimization problem by representing the feasible space in terms of meta-variables, each of which is a linear combination of the original variables. By training a low-dimensional surrogate model end-to-end, and jointly with the predictive model, we achieve: i) a large reduction in training and inference time; and ii) improved performance by focusing attention on the more important variables in the optimization and learning in a smoother space. Empirically, we demonstrate these improvements on a non-convex adversary modeling task, a submodular recommendation task and a convex portfolio optimization task.
Network security games (NSGs) are widely used in security related domain to model the interaction between the attacker and the defender. However, due to the complex graph structure of the entire network, finding a Nash equilibrium even when the attacker is fully rational is not well-studied yet. There is no efficient algorithms known with valid guarantees. We identify two major issues of NSGs: i) non-linearity ii) correlation between edges. NSGs with non-linear objective function are usually hard to optimize, while correlated edges might create exponentially many strategies and impact the scalability. In this paper, we analyze the distortion of linear and non-linear formulations of NSGs with fully rational attacker. We provide theoretical bounds on these different formulations, which can quantify the approximation ratio between linear and non-linear assumption. This result can help us understand how much loss will the linearization incur in exchange for the scalability.
Previous approaches to adversary modeling in network security games (NSGs) have been caught in the paradigm of first building a full adversary model, either from expert input or historical attack data, and then solving the game. Motivated by the need to disrupt the multibillion dollar illegal smuggling networks, such as wildlife and drug trafficking, this paper introduces a fundamental shift in learning adversary behavior in NSGs by focusing on the accuracy of the model using the downstream game that will be solved. Further, the paper addresses technical challenges in building such a game-focused learning model by i) applying graph convolutional networks to NSGs to achieve tractability and differentiability and ii) using randomized block updates of the coefficients of the defender's optimization in order to scale the approach to large networks. We show that our game-focused approach yields scalability and higher defender expected utility than models trained for accuracy only.