Learning Opposites Using Neural Networks

Many research works have successfully extended algorithms such as evolutionary algorithms, reinforcement agents and neural networks using "opposition-based learning" (OBL). Two types of the "opposites" have been defined in the literature, namely \textit{type-I} and \textit{type-II}. The former are linear in nature and applicable to the variable space, hence easy to calculate. On the other hand, type-II opposites capture the "oppositeness" in the output space. In fact, type-I opposites are considered a special case of type-II opposites where inputs and outputs have a linear relationship. However, in many real-world problems, inputs and outputs do in fact exhibit a nonlinear relationship. Therefore, type-II opposites are expected to be better in capturing the sense of "opposition" in terms of the input-output relation. In the absence of any knowledge about the problem at hand, there seems to be no intuitive way to calculate the type-II opposites. In this paper, we introduce an approach to learn type-II opposites from the given inputs and their outputs using the artificial neural networks (ANNs). We first perform \emph{opposition mining} on the sample data, and then use the mined data to learn the relationship between input $x$ and its opposite $\breve{x}$. We have validated our algorithm using various benchmark functions to compare it against an evolving fuzzy inference approach that has been recently introduced. The results show the better performance of a neural approach to learn the opposites. This will create new possibilities for integrating oppositional schemes within existing algorithms promising a potential increase in convergence speed and/or accuracy.Comment: To appear in proceedings of the 23rd International Conference on Pattern Recognition (ICPR 2016), Cancun, Mexico, December 201

Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression

Developing mathematical models of dynamic systems is central to many disciplines of engineering and science. Models facilitate simulations, analysis of the system's behavior, decision making and design of automatic control algorithms. Even inherently model-free control techniques such as reinforcement learning (RL) have been shown to benefit from the use of models, typically learned online. Any model construction method must address the tradeoff between the accuracy of the model and its complexity, which is difficult to strike. In this paper, we propose to employ symbolic regression (SR) to construct parsimonious process models described by analytic equations. We have equipped our method with two different state-of-the-art SR algorithms which automatically search for equations that fit the measured data: Single Node Genetic Programming (SNGP) and Multi-Gene Genetic Programming (MGGP). In addition to the standard problem formulation in the state-space domain, we show how the method can also be applied to input-output models of the NARX (nonlinear autoregressive with exogenous input) type. We present the approach on three simulated examples with up to 14-dimensional state space: an inverted pendulum, a mobile robot, and a bipedal walking robot. A comparison with deep neural networks and local linear regression shows that SR in most cases outperforms these commonly used alternative methods. We demonstrate on a real pendulum system that the analytic model found enables a RL controller to successfully perform the swing-up task, based on a model constructed from only 100 data samples