The algorithm weanalyze performs online updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counterexamples with regards to the Significance of online updating and linearly parameterized function approximators. 1 INTRODUCTION The problem of predicting the expected long-term future cost (or reward) of a stochastic dynamic system manifests itself in both time-series prediction and control. Anexample in time-series prediction is that of estimating the net present value of a corporation, as a discounted sum of its future cash flows, based on the current state of its operations. In control, the ability to predict long-term future cost as a function of state enables the ranking of alternative states in order to guide decision-making. Indeed, such predictions constitute the cost-to-go function that is central to dynamic programming and optimal control (Bertsekas, 1995). Temporal-difference learning, originally proposed by Sutton (1988), is a method for approximating long-term future cost as a function of current state.

Large dots indicate SVs .

Brake forming is widely applied in the high variety and small batch part manufacturing of sheet metal components, for the bending of straight bending lines. Currently, the planning of the bending sequences is a task that has to be performed manually, involving many heuristic criteria. However, set-up and bend sequencing procedures and knowledge have to be formally formalized and modeled, for the development of computer-aided process planning systems for sheet metal forming. This paper describes the application of fuzzy set theory for the normalization and modeling of the set-up and bend sequencing process for sheet metal bending. A fuzzy-set based methodology is used to determine the optimal bending sequences for the brake forming of sheet metal components, taking into account the relative importance of handling and accuracy.

We develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the degree of approximation, and the potential utility of the data points towards optimizing this objective. We show how the general strategy can be used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empirical results to suggest that this is the case. 1 INTRODUCTION AND MOTIVATION Learning from examples is a common supervised learning paradigm that hypothesizes a target concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesizing an approximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source.

We develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the degree of approximation, and the potential utility of the data points towards optimizing this objective. We show how the general strategy can be used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empirical results to suggest that this is the case. 1 INTRODUCTION AND MOTIVATION Learning from examples is a common supervised learning paradigm that hypothesizes a target concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesizing an approximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source.

We develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the degree ofapproximation, and the potential utility of the data points towards optimizing this objective. We show how the general strategy canbe used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empirical resultsto suggest that this is the case. 1 INTRODUCTION AND MOTIVATION Learning from examples is a common supervised learning paradigm that hypothesizes atarget concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesizing anapproximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source. By judiciously selecting ex- 594 KahKay Sung, Parlha Niyogi amples instead of allowing for possible random sampling, active learning techniques can conceivably have faster learning rates and better approximation results than passive learning methods. This paper presents a Bayesian formulation for active learning within the function approximation framework.

Such decisions include which function approximator to use, how to trade smoothness for goodness of fit and which features are relevant.

Such decisions include which function approximator to use, how to trade smoothness for goodness of fit and which features are relevant.

Such decisions include which function approximator to use, how to trade smoothness for goodness of fit and which features arerelevant.

This article summarizes the findings of a 1992 study of knowledge-based systems research and applications in Japan. Representatives of universities and businesses were chosen by the Japan Technology Evaluation Center to investigate the state of the technology in Japan relative to the United States. The panel's report focused on applications, tools, and research and development in universities and industry and on major national projects.