A Theoretical Framework for Target Propagation

The success of deep learning, a brain-inspired form of AI, has sparked interest in understanding how the brain could similarly learn across multiple layers of neurons. However, the majority of biologically-plausible learning algorithms have not yet reached the performance of backpropagation (BP), nor are they built on strong theoretical foundations. Here, we analyze target propagation (TP), a popular but not yet fully understood alternative to BP, from the standpoint of mathematical optimization. Our theory shows that TP is closely related to Gauss-Newton optimization and thus substantially differs from BP. Furthermore, our analysis reveals a fundamental limitation of difference target propagation (DTP), a well-known variant of TP, in the realistic scenario of non-invertible neural networks. We provide a first solution to this problem through a novel reconstruction loss that improves feedback weight training, while simultaneously introducing architectural flexibility by allowing for direct feedback connections from the output to each hidden layer. Our theory is corroborated by experimental results that show significant improvements in performance and in the alignment of forward weight updates with loss gradients, compared to DTP.Comment: 13 pages and 4 figures in main manuscript; 41 pages and 8 figures in supplementary materia

Supervised classification by multilayer networks

The Multi-Layer Perceptron (PMC in French) is one of the neural networks the most widely used, particularly for supervised classification . First, existing results on general representation capabilities enjoyed by the PMC architecture are surveyed, independently of any learning algorithm . Then it is shown why the minimization of a quadratic error over the learning set seems an awkward optimization criterion, though some asymptotic properties are also proved . In a second stage, the bayesian approach is analyzed when leaming sets offinite size are at disposai. ~ith the help of certain density estimators whose basic properties are emphasized, it is possible to build a feed forward neural network implementing the bayesian classification . This technique of direct discrimination seems to perform better Chan the classical MLP in all respects despite of the similarities of the architectures .Le Perceptron MultiCouche (PMC) est un des réseaux de neurones les plus utilisés actuellement, pour la classification supervisée notamment. On fait dans un premier temps une synthèse des résultats acquis en matière de capacités de représentation dont jouit potentiellement l'architecture PMC, indépendamment de tout algorithme d'apprentissage. Puis on montre pourquoi la minimisation d'une erreur quadratique sur la base d'apprentissage semble être un critère mal approprié, bien que certaines propriétés asymptotiques soient aussi exhibées. Dans un second temps, l'approche bayésienne est analysée lorsqu'on ne dispose que d'une base d'apprentissage de taille fini

Applications of Machine Learning in Supply Chains

Advances in new technologies have resulted in increasing the speed of data generation and accessing larger data storage. The availability of huge datasets and massive computational power have resulted in the emergence of new algorithms in artificial intelligence and specifically machine learning, with significant research done in fields like computer vision. Although the same amount of data exists in most components of supply chains, there is not much research to utilize the power of raw data to improve efficiency in supply chains.In this dissertation our objective is to propose data-driven non-parametric machine learning algorithms to solve different supply chain problems in data-rich environments.Among wide range of supply chain problems, inventory management has been one of the main challenges in every supply chain. The ability to manage inventories to maximize the service level while minimizing holding costs is a goal of many company. An unbalanced inventory system can easily result in a stopped production line, back-ordered demands, lost sales, and huge extra costs. This dissertation studies three problems and proposes machine learning algorithms to help inventory managers reduce their inventory costs.In the first problem, we consider the newsvendor problem in which an inventory manager needs to determine the order quantity of a perishable product to minimize the sum of shortage and holding costs, while some feature information is available for each product. We propose a neural network approach with a specialized loss function to solve this problem. The neural network gets historical data and is trained to provide the order quantity. We show that our approach works better than the classical separated estimation and optimization approaches as well as other machine learning based algorithms. Especially when the historical data is noisy, and there is little data for each combination of features, our approach works much better than other approaches. Also, to show how this approach can be used in other common inventory policies, we apply it on an $(r,Q)$ policy and provide the results.This algorithm allows inventory managers to quickly determine an order quantity without obtaining the underling demand distribution.Now, assume the order quantities or safety stock levels are obtained for a single or multi-echelon system. Classical inventory optimization models work well in normal conditions, or in other words when all underlying assumptions are valid. Once one of the assumptions or the normal working conditions is violated, unplanned stock-outs or excess inventories arise.To address this issue, in the second problem, a multi-echelon supply network is considered, and the goal is to determine the nodes that might face a stock-out in the next period. Stock-outs are usually expensive and inventory managers try to avoid them, so stock-out prediction might results in averting stock-outs and the corresponding costs.In order to provide such predictions, we propose a neural network model and additionally three naive algorithms. We analyze the performance of the proposed algorithms by comparing them with classical forecasting algorithms and a linear regression model, over five network topologies. Numerical results show that the neural network model is quite accurate and obtains accuracies in $[0.92, 0.99]$ for the hardest to easiest network topologies, with average of 0.950 and standard deviation of 0.023, while the closest competitor, i.e., one of the proposed naive algorithms, obtains accuracies in $[0.91, 0.95]$ with average of 9.26 and standard deviation of .0136. Additionally, we suggest conditions under which each algorithm is the most reliable and additionally apply all algorithms to threshold and multi-period predictions.Although stock-out prediction can be very useful, any inventory manager would like to have a powerful model to optimize the inventory system and balance the holding and shortage costs. The literature on multi-echelon inventory models is quite rich, though it mostly relies on the assumption of accessing a known demand distribution. The demand distribution can be approximated, but even so, in some cases a globally optimal model is not available.In the third problem, we develop a machine learning algorithm to address this issue for multi-period inventory optimization problems in multi-echelon networks. We consider the well-known beer game problem and propose a reinforcement learning algorithm to efficiently learn ordering policies from data.The beer game is a serial supply chain with four agents, i.e. retailer, wholesaler, distributor, and manufacturer, in which each agent replenishes its stock by ordering beer from its predecessor. The retailer satisfies the demand of external customers, and the manufacturer orders from external suppliers. Each of the agents must decide its own order quantity to minimize the summation of holding and shortage cost of the system, while they are not allowed to share any information with other agents. For this setting, a base-stock policy is optimal, if the retailer is the only node with a positive shortage cost and a known demand distribution is available. Outside of this narrow condition, there is not a known optimal policy for this game. Also, from the game theory point of view, the beer game can be modeled as a decentralized multi-agent cooperative problem with partial observability, which is known as a NEXP-complete problem.We propose an extension of deep Q-network for making decisions about order quantities in a single node of the beer game. When the co-players follow a rational policy, it obtains a close-to-optimal solution, and it works much better than a base-stock policy if the other agents play irrationally. Additionally, to reduce the training time of the algorithm, we propose using transfer learning, which reduces the training time by one order of magnitude. This approach can be extended to other inventory optimization and supply chain problems

Applications of neural networks to control systems

Tese de dout., Engenharia Electrónica, School of Electronic Engineering Science, Univ. of Wales, Bangor, 1992This work investigates the applicability of artificial neural networks to control systems. The following properties of neural networks are identified as of major interest to this field: their ability to implement nonlinear mappings, their massively parallel structure and their capacity to adapt. Exploiting the first feature, a new method is proposed for PID autotuning. Based on integral measures of the open or closed loop step response, multilayer perceptrons (MLPs) are used to supply PID parameter values to a standard PID controller. Before being used on-line, the MLPs are trained offline, to provide PID parameter values based on integral performance criteria. Off-line simulations, where a plant with time-varying parameters and time varying transfer function is considered, show that well damped responses are obtained. The neural PID autotuner is subsequently implemented in real-time. Extensive experimentation confirms the good results obtained in the off-line simulations. To reduce the training time incurred when using the error back-propagation algorithm, three possibilities are investigated. A comparative study of higherorder methods of optimization identifies the Levenberg-Marquardt (LM)algorithm as the best method. When used for function approximation purposes, the neurons in the output layer of the MLPs have a linear activation function. Exploiting this linearity, the standard training criterion can be replaced by a new, yet equivalent, criterion. Using the LM algorithm to minimize this new criterion, together with an alternative form of Jacobian matrix, a new learning algorithm is obtained. This algorithm is subsequently parallelized. Its main blocks of computation are identified, separately parallelized, and finally connected together. The training time of MLPs is reduced by a factor greater than 70 executing the new learning algorithm on 7 Inmos transputers