Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training

A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the momentum-less AdaGrad method as a particular (single-level) instance. The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to noise, while the multi-level feature aims at reducing their computational cost. The evaluation complexity of these algorithms is analyzed and their behaviour in the presence of noise is then illustrated in the context of training deep neural networks for supervised learning applications.Comment: 29 pages, 4 figure

Genetic programming and bacterial algorithm for neural networks and fuzzy systems design

In the field of control systems it is common to use techniques based on model adaptation to carry out control for plants for which mathematical analysis may be intricate. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this line, this paper gives a perspective on the quality of results given by two different biologically connected learning algorithms for the design of B-spline neural networks (BNN) and fuzzy systems (FS). One approach used is the Genetic Programming (GP) for BNN design and the other is the Bacterial Evolutionary Algorithm (BEA) applied for fuzzy rule extraction. Also, the facility to incorporate a multi-objective approach to the GP algorithm is outlined, enabling the designer to obtain models more adequate for their intended use

Multi objective genetic algorithm for training three term backpropagation network

Multi Objective Evolutionary Algorithms has been applied for learning problem in Artificial Neural Networks to improve the generalization of the training and testing unseen data.This paper proposes the simultaneous optimization method for training Three Term Back Propagation Network (TTBPN) learning using Multi Objective Genetic Algorithm.The Non-dominated Sorting Genetic Algorithm II is applied to optimize the TTBPN structure by simultaneously reducing the error and complexity in terms of number of hidden nodes of the network for better accuracy in classification problem.This methodology is applied in two kinds of multiclasses data set obtained from the University of California at Irvine repository.The results obtained for training and testing on the datasets illustrate less network error and better classification accuracy, besides having simple architecture for the TTBPN

Sampling-based probabilistic inference emerges from learning in neural circuits with a cost on reliability

Neural responses in the cortex change over time both systematically, due to ongoing plasticity and learning, and seemingly randomly, due to various sources of noise and variability. Most previous work considered each of these processes, learning and variability, in isolation -- here we study neural networks exhibiting both and show that their interaction leads to the emergence of powerful computational properties. We trained neural networks on classical unsupervised learning tasks, in which the objective was to represent their inputs in an efficient, easily decodable form, with an additional cost for neural reliability which we derived from basic biophysical considerations. This cost on reliability introduced a tradeoff between energetically cheap but inaccurate representations and energetically costly but accurate ones. Despite the learning tasks being non-probabilistic, the networks solved this tradeoff by developing a probabilistic representation: neural variability represented samples from statistically appropriate posterior distributions that would result from performing probabilistic inference over their inputs. We provide an analytical understanding of this result by revealing a connection between the cost of reliability, and the objective for a state-of-the-art Bayesian inference strategy: variational autoencoders. We show that the same cost leads to the emergence of increasingly accurate probabilistic representations as networks become more complex, from single-layer feed-forward, through multi-layer feed-forward, to recurrent architectures. Our results provide insights into why neural responses in sensory areas show signatures of sampling-based probabilistic representations, and may inform future deep learning algorithms and their implementation in stochastic low-precision computing systems

Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems

Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA

Pareto multi-task deep learning

Neuroevolution has been used to train Deep Neural Networks on reinforcement learning problems. A few attempts have been made to extend it to address either multi-task or multi-objective optimization problems. This research work presents the Multi-Task Multi-Objective Deep Neuroevolution method, a highly parallelizable algorithm that can be adopted for tackling both multi-task and multi-objective problems. In this method prior knowledge on the tasks is used to explicitly define multiple utility functions, which are optimized simultaneously. Experimental results on some Atari 2600 games, a challenging testbed for deep reinforcement learning algorithms, show that a single neural network with a single set of parameters can outperform previous state of the art techniques. In addition to the standard analysis, all results are also evaluated using the Hypervolume indicator and the Kullback-Leibler divergence to get better insights on the underlying training dynamics. The experimental results show that a neural network trained with the proposed evolution strategy can outperform networks individually trained respectively on each of the tasks