Mathematical Learning Models — Theory and Algorithms: Proceedings of a Conference

This volume contains most of the contributions presented at the conference "Mathematical Learning Models - Theory and Algorithms". The conference was organized by the Institute of Applied Mathematics of the University of Bonn under the auspices of the Sonderforschungs­ bereich 72. It took place in the Physikzentrum in Bad Honnef near to Bonn from May 3 - May 7, 1982. The idea of the organizers was to bring together experts who work on very related problems, but partially by using different approaches. The main subjects of the program were: - mathematical learning models, - bandit problems, - stochastic approximation procedures, - sequential decision processes with unknown law of nature. We felt that in a sense "learning" was a common concept for all these branches. In the contributions the state of the art in the above topics was presented from different pOints of view with special regard to recent advances. The exchange of results and opinions was continued in many fruitful and vivid discussions. The atmosphere of the conference center offered a suitable and pleasant framework for the scientific program. We express our gratitude to all contributors for making the con­ ference successful. Simultaneously we hope that further work on the above mentioned field has been stimulated.

Table of Contents:
The Minimax Risk for the Two-Armed Bandit Problem.- Bandit Problems with Random Discounting.- Stochastic Approximation on a Bounded Convex Set.- Learning Automaton for Finite Semi-Markov Decision Processes.- A Local Asymptotic Minimax Optimality of an Adaptive Robbins-Monro Stochastic Approximation Procedure.- Dynamic Allocation Indices for Bayesian Bandits.- The Role of Dynamic Allocation Indices in the Evaluation of Suboptimal Strategies for Families of Bandit Processes.- On the Discretization Technique for Optimal Discounted Control of the Wiener Process.- Asymptotic Properties of Learning Models.- On the Infinitesimal Characterization of Monotone Stopping Problems in Continuous Time.- Numerical Investigation of the Two-Armed Bandit.- Uniform Bounds for a Dynamic Programming Model under Adaptive Control Using Exponentially Bounded Error Probabilities.- Stochastic Regression Models and Consistency of the Least Squares Identification Scheme.- Recursive Identification Techniques.- An Optimization Problem for Matrices with Application to Decision Models.- On a Class of Learning Algorithms with Symmetric Behavior under Success and Failure.- Convergence of a General Stochastic Approximation Process under Convex Constraints and Some Applications.- On Kersting’s Theorem on Weak Convergence of Recursions.- On Continuous Time Learning Models.- Convergence of Stochastic Approximation Algorithms with Non-Additive Dependent Disturbances and Applications.- Sequential Probability Ratio Tests for Homogeneous Markov Chains.- Allocation Rules for Sequential Clinical Trials.- Non-Deterministic Modelling and its Application in Adaptive Optimal Control.