J. Poland and K. Knödler
Radial basis functions, compact support, confidence term, active learning, model-based optimization
Building models for any kind of complex process is an important tool of today’s applied computer science. There are many situations where the trust in the model varies over the input space, and where the amount of trust or confidence should significantly affect the behaviour of the model and the resulting decisions (this applies when the model is used within some decision process, e.g., in a control or optimization task). In this paper, we will focus on special one-sided situations where overestimating the true process is considered critical, while underestimating is tolerable (or conversely). We introduce a new type of radial basis function, the confidence term, with the following properties: (a) it is smooth, i.e., infinitely differentiable and (b) compactly supported. We show how one-sided trust control can be achieved for any kind of model by a simple multiplication with the confidence term. To demonstrate the power and flexibility of our approach, two quite different applications are presented, both of which are practically relevant. One is model-based optimization with constraints, where we have to be careful not to narrow the search space too quickly, until we can trust the constraint model. This requires imposing a low confidence on the constraint model until enough data is available. In the other application, active learning with multiple point queries, we need to achieve the opposite and impose a high value of trust in regions that have been already explored.
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