Regret Minimisation in Multi-Armed Bandits Using Bounded Arm Memory

In this paper, we propose a constant word (RAM model) algorithm for regret minimisation for both finite and infinite Stochastic Multi-Armed Bandit (MAB) instances. Most of the existing regret minimisation algorithms need to remember the statistics of all the arms they encounter. This may become a problem for the cases where the number of available words of memory is limited. Designing an efficient regret minimisation algorithm that uses a constant number of words has long been interesting to the community. Some early attempts consider the number of arms to be infinite, and require the reward distribution of the arms to belong to some particular family. Recently, for finitely many-armed bandits an explore-then-commit based algorithm~\citep{Liau+PSY:2018} seems to escape such assumption. However, due to the underlying PAC-based elimination their method incurs a high regret. We present a conceptually simple, and efficient algorithm that needs to remember statistics of at most $M$ arms, and for any $K$-armed finite bandit instance it enjoys a $O(KM +K^{1.5}\sqrt{T\log (T/MK)}/M)$ upper-bound on regret. We extend it to achieve sub-linear \textit{quantile-regret}~\citep{RoyChaudhuri+K:2018} and empirically verify the efficiency of our algorithm via experiments

Orbital symmetry of a triplet pairing in a heavy Fermion superconductor UPt_3

The orbital symmetry of the superconducting order parameter in UPt_3 is identified by evaluating the directionally dependent thermalconductivity and ultrasound attenuation in the clean limit and compared with the existing data for both basal plane and the c-axis of a hexagonal crystal. The resulting two component orbital part expressed by (\lambda_x(k), \lambda_y(k)) is combined with the previously determined triplet spin part, leading to clean limit and compared with the existing data for both basal plane and the c-axis of a hexagonal crystal. The resulting two component orbital part expressed by (\lambda_x(k), \lambda_y(k)) is combined with the previously determined triplet spin part, leading to the order parameter of either the non-unitary bipolar state of the form: d(k) = b \lambda_x(k) + i j \lambda_y(k) or the unitary planar state of the form: d(k) = b \lambda_x(k) + j \lambda_y(k) where b \perp j = c, or a with the hexagonal unit vectors a, b and c. The d vector is rotatable in the plane spanned by a and c perpendicular to b under weak applied c-axis field because of the weak spin orbit coupling. Experiments are proposed to distinguish between the equally possible these states.Comment: 8 pages, 8 eps figure

Totem: An embodiment of human character and personality in footwear design

This thesis is an attempt at drawing parallels between human character traits and footwear design as an evocative means to communicate character. The idea here is to translate qualitative elements of personality traits and communicate expressions through the embodiment of meaning within form in the context of footwear design. I am making an attempt at equating the meaning in form and footwear gestures that serve an emotional or functional purpose in footwear to break down the sculpture into a combination of different attributes so as to create a character taxonomy. This character taxonomy serves the purpose of assisting me in the creation of the generative system by defining its parameters in numerical values in Grasshopper. The Generative System - Totem uses these values to create sculptural surfaces that are derived from consumer character inputs and are thus, personal to every individual. Through this book, I am taking you through my journey of investigation to better tell personal human stories through footwear - a product that is an extension of one’s personality and footwear design as a form of expression