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.Expand

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.Expand

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.Expand

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… Expand

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,… Expand

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… Expand

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… Expand