A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Near infrared optical materials from polymeric amorphous carbon synthesized by collisional plasma process

The synthesis of polymerlike amorphous carbon(a-C:H) thin-films by microwave excited collisional hydrocarbon plasma process is reported. Stable and highly aromatic a-C:H were obtained containing significant inclusions of poly(p-phenylene vinylene) (PPV). PPV confers universal optoelectronic properties to the synthesized material. That is a-C:H with tailor-made refractive index are capable of becoming absorption-free in visible (red)-near infrared wavelength range. Production of large aromatic hydrocarbon including phenyl clusters and/or particles is attributed to enhanced coagulation of elemental plasma species under collisional plasma conditions. Detailed structural and morphological changes that occur in a-C:H during the plasma synthesis are also described.

Indigenous mathematics : creating an equitable learning environment

This chapter examines how a change in school leadership can successfully address competencies in complex situations and thus create a positive learning environment in which Indigenous students can excel in their learning rather than accept a culture that inhibits school improvement. Mathematics has long been an area that has failed to assist Indigenous students in improving their learning outcomes, as it is a Eurocentric subject (Rothbaum, Weisz, Pott, Miyake & Morelli, 2000, De Plevitz, 2007) and does not contextualize pedagogy with Indigenous culture and perspectives (Matthews, Cooper & Baturo, 2007). The chapter explores the work of a team of Indigenous and non-Indigenous academics from the YuMi Deadly Centre who are turning the tide on improving Indigenous mathematical outcomes in schools and in communities with high numbers of Aboriginal and Torres Strait Islander students.

Yorkshire Cities and Culture : A Review of Current Thinking

This report was commissioned by the Yorkshire Cultural Observatory and the Yorkshire & Humber Key Cities group. It is not a strategy document but an attempt to give an overview of the current thinking within academia and policy-making about the cultural agenda for regions and regional cities in the UK. In particular it looks at the challenges for Yorkshire cities in the context of the current and potential regional cultural offer. The report is a snapshot of current academic and policy thinking, but it also draws on a series of interviews conducted with policymakers in the five key cities as well as regional agencies. These interviews were limited in number and are not meant to be a comprehensive consultation exercise. Rather they acted to focus some of the issues raised by the literature and policy review and to develop suggestions around priority areas for the region.

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand’s concentration inequality for empirical processes.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

The causes and consequences of corruption

This thesis comprehensively studies the causes and consequences of corruption in both crosscountry and within-country contexts, mainly focusing on China. The thesis commences by extensively investigating the causes of corruption. Using the standard economic approach, this study finds that in China regions with more anti-corruption efforts, higher education attainment, Anglo-American historic influence, higher openness, more access to media, higher relative wages of government employees, and a greater representation of women in legislature are markedly less corrupt; while the social heterogeneity, deregulation and abundance of resources, substantially breed regional corruption. Moreover, fiscal decentralization is discovered to depress corruption significantly. This study also observes a positive relationship between corruption and the economic development in current China that is mainly driven by the transition to a market economy. Focusing on the influence of political institutions on corruption, the thesis then provides evidence that a high level of political interest helps to reduce corruption within a society, while the effect of democracy upon corruption depends on property rights protection and income distribution. With the social economic approach, however, the thesis presents both cross-country and within-country evidence that the social interaction plays an important role in determining corruption. The thesis then continues by comprehensively evaluating the consequences of corruption in China. The study provides evidence that corruption can simultaneously have both positive and negative effects on economic development. And it also observes that corruption considerably increases the income inequality in China. Furthermore this study finds that corruption in China significantly distorts public expenditures. Local corruption is also observed to substantially reduce FDI in Chinese regions. Finally the study documents that corruption substantially aggravates pollution probably through a loosening of the environmental regulation, and that it also modifies the effects of trade openness and FDI on the stringency of environmental policy. Overall, this thesis adds to the current literature by a number of novel findings concerning both the causes and the consequences of corruption.