Online Performance-Improvement Algorithms

TL;DR: Algorithms for improving performance at other tasks, such as navigation and and paging, and an online navigation algorithm for a robot traveling back and forth between two points s and t in a scene filled with unknown axis-parallel rectangular obstacles are presented.

Abstract: The results presented in this thesis contribute to two areas of computer science: machine learning and on-line algorithms. One limitation of current theoretical approaches to learning is that most of them involve function approximation, i.e., the learner improves the accuracy of its approximation to an unknown function as it sees more samples of the function. This thesis presents algorithms for improving performance at other tasks, such as navigation and and paging. Specifically, these algorithms are online algorithms whose competitiveness improves when repeatedly applied to the same problem. The design of such algorithms is a new challenge in the area of online algorithms: the algorithms must not only be competitive on each application, but must also acquire useful information to improve their future competitiveness. We present a general framework based on task systems for studying such algorithms. One result in the thesis is an online navigation algorithm for a robot traveling back and forth between two points s and t (distance n apart) in a scene filled with unknown axis-parallel rectangular obstacles. For each i > n, the ith trip of the robot is guaranteed to be within a - ___ O(/n/i) factor of the shortest s-t path length L, and we show that up to constant factors this is the best a deterministic algorithm can do. This algorithm is based on a smooth search-quality tradeoff: we design ____ an algorithm that given any k > n, searches a distance O(L /n/k) and - finds an s-t path of length O(L /n/k). A key insight is that this tradeoff can be achieved by optimally traversing a certain tree structure based on the obstacles. For a version of the paging problem where the pager is aware only of page faults, we give an algorithm whose average competitiveness improves when the same page request sequence is repeated several times. The thesis also applies competitive analysis to design an online algorithm for a natural extension of the standard function prediction problem, where the function labeling the examples switches unpredictably between two unknown functions.