TR 2:30-4, 37-232Over the last few years there has been rapidly expanded interest in complex engineering problems in areas ranging from signal processing, pattern recognition and control theory, all the way to applications in logistics and finance. Such problems often involve high dimensional systems (the "curse of dimensionality") or highly nonlinear, sometimes ill-defined models. While little progress can be made on such problems using classical methods, there has been recently an explosion of methods based on artificial neural networks and related approximation techniques that have greatly expanded the scope of solvable problems. These methods have generated much excitement and publicity, and have significant practical use.
Prof. Dimitri Bertsekas, 35-210, x7267
3-0-9
Prerequisites: Linear algebra, probability, and at least one graduate course in applied probability, optimization, or control
The objective of this course is to cover the foundation of neural network techniques as well as their application to specific problem domains. While the successful use of neural network methods contains a certain element of "art," there is also an accumulated body of knowledge whose understanding provides a useful guide into applications, and enables a critical appraisal of the sometimes inflated and conflicting claims regarding the potential of the neural network technology.
The course will provide a balanced approach between the art and the science of neural networks. On the methodological side, it covers different neural network architectures and the associated training algorithms; how to use neural network methods in areas like classification, nonlinear estimation and system identification, and nonlinear control. Special emphasis is placed on the subject of neuro-dynamic programming, which is a combination of (a) traditional methods for decision making under uncertainty and stochastic control and (b) neural networks and other methods for dimensionality reduction. On the application side, there will be several examples to illustrate the use of the different methods in specific domains (for example, communications and logistics) and to amplify some of the issues that are important in practice.
Course Contents:
1. Introduction: Models, data, and learning.
2. Pattern recognition: Linear classifiers. Perceptions and the perceptron learning theorem. Statistical and neural network approaches to the classification problem.
3. Multilayer perceptrons and other architectures: Universal approximation property. Gradient computation via backpropagation. Other architectures: feature extraction, linear architectures and basis function representations; radial basis functions.
4. Parameter estimation and system identification: Applications in control and signal processing.
5. Neural network training methods: Iterative descent. Convergence and convergence rate. Descent methods with errors. Incremental gradient methods for least squares. Extended Kalman filter. Stochastic approximation methods.
6. Uses of neural networks in control: Recurrent backpropagation. Model reference adaptive control. Backpropagation through time. Learning from an expert.
7. Introduction to dynamic programming: Problem taxonomy. Bellman's equation. Classical computational methods for dynamic programming problems: value iteration, policy iteration, hybrid methods.
8. Simulation-based methods for dynamic programming: Temporal differences. Q-learning.
9. Neuro-dynamic programming using neural network approximations: Feature-based aggregation. Bellman error methods. Approximate policy iteration.
Texts: A set of notes on Neuro-Dynamic Programming by D. Bertsekas and J. Tsitsiklis
S. Haykin, Neural Networks, Prentice Hall, 1994. Recommended text, available at the Coop
D. Bertsekas, Nonlinear Programming, Athena Scientific, 1995. Recommended text, available at the Coop
There will be 4-5 homeworks and a term paper or project.
|
Created: Dec 12, 1995
|
Modified: Dec 12, 1995|
Your comments
and inquiries are welcome.