Evolutionary algorithms (EAs) are general-purpose optimization algorithms, inspired by natural evolution. Recent theoretical studies have shown that EAs can achieve good approximation guarantees for solving the problem classes of submodular optimization, which have a wide range of applications, such as maximum coverage, sparse regression, influence maximization, document summarization and sensor placement, just to name a few. Though they have provided some theoretical explanation for the general-purpose nature of EAs, the considered submodular objective functions are defined only over sets or multisets. To complement this line of research, this paper studies the problem class of maximizing monotone submodular functions over sequences, where the objective function depends on the order of items. We prove that for each kind of previously studied monotone submodular objective functions over sequences, i.e., prefix monotone submodular functions, weakly monotone and strongly submodular functions, and DAG monotone submodular functions, a simple multi-objective EA, i.e., GSEMO, can always reach or improve the best known approximation guarantee after running polynomial time in expectation. Note that these best-known approximation guarantees can be obtained only by different greedy-style algorithms before.

There is a lot of hype today about deep learning, a class of multilayer perceptrons with some 5-20 layers featuring convolutional and polling layers. Many blogs [1,2,3] discuss the structure of these networks, there is plenty code published so I won't get into much detail here. Several tech companies had invested a lot of money into this research and everyone has very high expectations on performance of these models. Indeed they've been winning image classification competitions for several years now and media are reporting superhuman performance on some visual classification tasks once in a while. Now just looking at the numbers from ImageNet competition is not really telling us much on how good these models really are, we can only maybe confirm that they are much better than whatever came before them (for that benchmark at least).