Bandits and Experts in Metric Spaces
- Computer ScienceJ. ACM
This work presents a solution for the multi-armed bandit problem, in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric, and presents an algorithm that comes arbitrarily close to meeting this bound.
Sharp dichotomies for regret minimization in metric spaces
- Computer Science, MathematicsSODA '10
It is proved that for every metric space, the optimal regret of a Lipschitz MAB algorithm is either bounded above by any f ε w(log t), or bounded below by any g √t, and the proof connects upper and lower bound techniques in online learning with classical topological notions such as perfect sets and the Cantor-Bendixson theorem.
Generation of Cantor sets from fractal squares : A mathematical prospective
- Computer ScienceJournal of Interdisciplinary Mathematics
Fractal square is focused on to generate cantor set by using its different topological properties in terms of disconnected fractal sets, designing the process of various patterns with the help of fractal square and to make a topological classification among them.
On the construction, properties and Hausdorff dimension of random Cantor one pth set
In 1883, German Mathematician George Cantor introduced Cantor ternary set which is a self-similar fractal. K. J. Falconer (1990) defined random Cantor set with statistical self-similarity. The…
Cantor and Continuity
Georg Cantor (1845-1919), with his seminal work on sets and number, brought forth a new field of inquiry, set theory, and ushered in a way of proceeding in mathematics, one at base infinitary,…
Cantor E I Cardinali
- Lettera Matematica Pristem
Trees, Refining, and Combinatorial Characteristics
Author(s): Galgon, Geoff | Advisor(s): Zeman, Martin | Abstract: The analysis of trees and the study of cardinal characteristics are both of historical and contemporary importance to set theory. In…
Minimal Cantor Sets: The Combinatorial Construction of Ergodic Families and Semi-Conjugations
Combinatorially obtained minimal Cantor sets are acquired as the inverse limit of certain directed topological graphs where specific nonnegative integer matrices, called winding matrices, are used to…