Subjective Mapping

Abstract

There are a variety of domains where it is desirable to learn a representation of an environment defined by a stream of sensori-motor experience. This dissertation introduces and formalizes subjective mapping, a novel approach to this problem. A learned representation is subjective if it is constructed almost entirely from the experience stream, minimizing the requirement of additional domain-specific information (which is often not readily obtainable).

In many cases the observational data may be too plentiful to be feasibly stored. In these cases, a primary feature of a learned representation is that it be compact---summarizing information in a way that alleviates storage demands. Consequently, the first key insight of the subjective mapping approach is to phrase the problem as a variation of the well-studied problem of dimensionality reduction. The second insight is that knowing the effects of actions is critical to the usefulness of a representation. Therefore enforcing that actions have a consistent and succinct form in the learned representation is also a key requirement.

This dissertation presents a new framework, action respecting embedding (ARE), which builds on a recent effective dimensionality reduction algorithm called maximum variance unfolding, in order to solve the newly introduced subjective mapping problem. The resulting learned representations are shown to be useful for reasoning, planning and localization tasks. At the heart of the new algorithm lies a semidefinite program leading to questions about ARE's ability to handle sufficiently large input sizes. The final contribution of this dissertation is to provide a divide-and-conquer algorithm as a first step to addressing this issue.