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This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures.These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area. 

The integrity of democratic elections depends on voters’ access to accurate information. However, modern media environments, which are dominated by social media, provide malicious actors with unprecedented ability to manipulate elections via misinformation, such as fake news. We study a zerosum game between an attacker, who attempts to subvert an election by propagating a fake new story or other misinformation over a set of advertising channels, and a defender who attempts to limit the attacker’s impact. Computing an equilibrium in this game is challenging as even the pure strategy sets of players are exponential. Nevertheless, we give provable polynomial-time approximation algorithms for computing the defender’s minimax optimal strategy across a range of settings, encompassing different population structures as well as models of the information available to each player. Experimental results confirm that our algorithms provide nearoptimal defender strategies and showcase variations in the difficulty of defending elections depending on the resources and knowledge available to the defender. 

Election control considers the problem of an adversary who attempts to tamper with a voting process, in order to either ensure that their favored candidate wins (constructive control) or another candidate loses (destructive control). As online social networks have become significant sources of information for potential voters, a new tool in an attacker’s arsenal is to effect control by harnessing social influence, for example, by spreading fake news and other forms of misinformation through online social media. We consider the computational problem of election control via social influence, studying the conditions under which finding good adversarial strategies is computationally feasible. We consider two objectives for the adversary in both the constructive and destructive control settings: probability and margin of victory (POV and MOV, respectively). We present several strong negative results, showing, for example, that the problem of maximizing POV is inapproximable for any constant factor. On the other hand, we present approxima- tion algorithms which provide somewhat weaker approximation guarantees, such as bicriteria approximations for the POV objective and constant-factor approximations for MOV. Finally, we present mixed integer programming formulations for these problems. Ex- perimental results show that our approximation algorithms often find near-optimal control strategies, indicating that election control through social influence is a salient threat to election integrity.