Skyline Identification in Multi-Armed Bandits

We introduce a variant of the classical PAC multi-armed bandit problem. There is an ordered set of $n$ arms $A[1],\dots,A[n]$, each with some stochastic reward drawn from some unknown bounded distribution. The goal is to identify the $skyline$ of the set $A$, consisting of all arms $A[i]$ such that $A[i]$ has larger expected reward than all lower-numbered arms $A[1],\dots,A[i-1]$. We define a natural notion of an $\varepsilon$-approximate skyline and prove matching upper and lower bounds for identifying an $\varepsilon$-skyline. Specifically, we show that in order to identify an $\varepsilon$-skyline from among $n$ arms with probability $1-\delta$, $$\Theta\bigg(\frac{n}{\varepsilon^2} \cdot \min\bigg\{ \log\bigg(\frac{1}{\varepsilon \delta}\bigg), \log\bigg(\frac{n}{\delta}\bigg) \bigg\} \bigg)$$ samples are necessary and sufficient. When $\varepsilon \gg 1/n$, our results improve over the naive algorithm, which draws enough samples to approximate the expected reward of every arm; the algorithm of (Auer et al., AISTATS'16) for Pareto-optimal arm identification is likewise superseded. Our results show that the sample complexity of the skyline problem lies strictly in between that of best arm identification (Even-Dar et al., COLT'02) and that of approximating the expected reward of every arm.Comment: 18 pages, 2 Figures; an ALT'18/ISIT'18 submissio

Letter to Father

Produced by The Center on Disability Studies, University of Hawai'i at Manoa, Honolulu, Hawai'i and The School of Social Sciences, The University of Texas at Dallas, Richardson, Texas for The Society for Disability Studies

Examining a First Grader’s Writing through a Habermasian Lens: Implications for the Teaching and Learning of Writing

This paper investigates the relationship between Habermas’s theory of communicative action (TCA) and writing. It begins with a review of the features of Habermas’s TCA: validity claims, their corresponding criteria, and the ideal speech situation. Then TCA is applied in analyzing a first grader’s written notes. Finally, the implications for the teaching and learning of writing are discussed from a Habermasian perspective. This paper demonstrates the applicability of Habermas’s TCA in examining writing. It also shows how TCA informs the teaching and learning of writing

Examining the Janus Face of Power in Critical Literacy Through a Habermasian Lens

This paper is concerned with the connection between the problematic of power in critical literacy and Jurgen Habermas’s theory of communicative action. It begins with a literature review of critical literacy to show that power can be oppressive or resisting/liberating. It argues that certain communicative parameters of Habermas’s theory of communicative action can be appropriated to address the oppressive and resisting/liberating aspects of power in critical literacy. This paper ends with a discussion of what power, relocated in Habermas’s framework, implies for critical literacy education

A Preliminary Look at the Physics Reach of a Solar Neutrino TPC: Time-Independent Two Neutrino Oscillations

This paper will discuss the physics reach of a solar neutrino TPC containing many tons of He4 under high pressure. Particular attention is given to the LMA and SMA solutions, which are allowed by current data, and which are characterized by a lack of time-dependent phenomena (either summer-winter or day-night asymmetries). In this case, the physics of neutrino masses and mixing is all contained in the energy dependence of the electron neutrino survival probability, (or in its reciprocal, the electron neutrino disappearance probability).Comment: 19 pages, 12 figure