Degeneracy in infinite horizon optimization

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon. We also present a general near-optimal forecast horizon.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47919/1/10107_2005_Article_BF01582295.pd

Integrating Constraint Solving into Proof Planning

In proof planning mathematical objects with theory-specific properties have to be constructed. More often than not, mere uni cation oers little support for this task. However, the integration of constraint solvers into proof planning can sometimes help solving this problem. We presen

Towards adaptive generation of faded examples

Faded examples have been investigated in pedagogical psychology. The experiments suggest that a learner can benefit from faded examples. For these experiments a few examples were faded manually. For realistic applications, however, it makes more sense to generate several variants of an exercise by fading a worked example and to do it automatically. For the automatic generation, a suitable knowledge representation of examples and exercises is required which we describe in the paper. Moreover, a user-adaptive system such as ActiveMath can select or dynamically produce faded example and present it to the student in response to her learning activities and adapted to her goals, capabilities, previous learning experience, etc. The structures and metadata in the knowledge representation of the examples are the basis for such an adaptation. The student model provides information for that adaptivity as well

Presenting Proofs with Adapted Granularity

When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user- and goal-adaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation based on classification. Expert knowledge for the classification task can be handauthored or extracted from annotated proof examples via machine learning techniques. The obtained models are employed for the automated generation of further proofs at an adapted level of granularity