Pareto analysis of evolutionary and learning systems

Abstract

Abstract-This paper attempts to argue that most adaptive systems, such as evolutionary or learning systems, have inherently multiple objectives to deal with. Very often, there is no single solution that can optimize all the objectives. In this case, the concept of Pareto optimality is key to analyzing these systems.To support this argument, we first present an example that considers the robustness and evolvability trade-off in a redundant genetic representation for simulated evolution. It is well known that robustness is critical for biological evolution, since without a sufficient degree of mutational robustness, it is impossible for evolution to create new functionalities. On the other hand, the genetic representation should also provide the chance to find new phenotypes, i.e., the ability to innovate. This example shows quantitatively that a trade-off between robustness and innovation does exist in the studied redundant representation.Interesting results will also be given to show that new insights into learning problems can be gained when the concept of Pareto optimality is applied to machine learning. In the first example, a Pareto-based multi-objective approach is employed to alleviate catastrophic forgetting in neural network learning. We show that learning new information and memorizing learned knowledge are two conflicting objectives, and a major part of both information can be memorized when the multiobjective learning approach is adopted. In the second example, we demonstrate that a Pareto-based approach can address neural network regularization more elegantly. By analyzing the Pareto-optimal solutions, it is possible to identifying interesting solutions on the Pareto front.

Using multiobjective optimization algorithms and decision making support to solve polymer extrusion problems

“…Solutions exhibiting little sensitivity to such variations are labelled as robust and are favored. Robustness is usually addressed either by optimizing the expectation and the variance , or by introducing additional constraints . The topic was reviewed by Jin and Branke and Beyer and Sendhoff .…”

Evolutionary multi-objective generation of recurrent neural network ensembles for time series prediction

“…The knee point is not located at the extremes and is of interest because it is believed that the complexity of the models in this region of the Pareto front matches that of the data [14,48] and that the models will not exhibit over-fitting on a validation data set. It is also hypothesized that models in this area will exhibit a smaller prediction variance.…”

Multi-objective optimization in machine learning

“…This thesis proposes a uniĄed framework for multi-objective modelling and training being applied to a vast set of classiĄcation tasks in machine learning. Despite the fact that multi-objective optimization methods are not widely used in machine learning, the literature is vast in approaches and scenarios being used to search for both interpretable and accurate models, models generated to have complementary properties, and conĆicting loss functions building ensembles (BRAGA et al, 2006;SENDHOFF, 2008;JIN et al, 2009). It is also used to model selection, ensemble generation, Ąltering, and aggregation (ZHOU, 2012); to the classiĄcation of imbalanced datasets (AKAN; SAYIN, 2014;GARCÍA et al, 2010); and to multi-task learning (BAGHERJEIRAN, 2007).…”

“…Out of the scope of multi-task learning, a possible solution for the weighting problem involving the loss functions of the whole set of tasks was proposed in Engen et al (2009), Wang et al (2014), approaching a multi-class classiĄcation by considering the minimization of the multiple learning losses, one for each class, as conĆicting objectives, thus resorting to a multi-objective optimization method. Supported by other scenarios when multi-objective optimization methods were used to solve machine learning problems (JIN; SENDHOFF, 2008;JIN et al, 2009), this work also conceives the learning losses as conĆicting objectives, but now under the framework of multi-task learning and explicitly adopting parameter sharing, a perspective that from the best of our knowledge still was unexplored.…”