Distributed Evolutionary Algorithms with Adversarial Corruption.

Evolutionary algorithms are inherently parallel optimization methods that have been successfully applied to many critical systems. While our understanding of their performance has steadily progressed, most existing work on distributed evolution assumes a perfect runtime environment. This assumption does not always hold in practice, and it is important to consider how robust such systems are to attack. We consider distributed evolutionary algorithms in a setting where a malicious adversary can confound the search process by corrupting the communication of candidate solutions in the distributed architecture. We study this setting for parallel evolutionary algorithms optimizing pseudo-Boolean functions under different adversarial models. We prove asymptotic bounds in various adversarial models that relate the number and budget of the adversary to success probability, solution quality and runtime on the ONEMAX problem. For a (1+lambda) EA running in a distributed master/worker architecture, we prove upper bounds on the slow-down incurred by adversarial attacks as a function of population size, number of compromised nodes and adversarial budget. For a (1,lambda) EA, we prove a negative result that reveals a parameter regime of the adversary that prevents efficient optimization. We also conduct experiments on ONEMAX and the combinatorial problem MAxCur. On the latter, we empirically find that (1,lambda) EA is more robust to adversarial corruption and, surprisingly, may even be able to leverage weak levels of corruption to outperform the adversary-free setting.