Polynomial-time Computation of Exact Correlated Equilibrium in Compact Games

In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm ("Ellipsoid Against Hope") for computing sample correlated equilibria of concisely-represented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to find an exact correlated equilibrium, but can be easily modified to efficiently compute approximate correlated equilibria. Currently, it remains unresolved whether the algorithm can be modified to compute an exact correlated equilibrium. We show that it can, presenting a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identification of exact correlated equilibrium. Our new algorithm differs from the original primarily in its use of a separation oracle that produces cuts corresponding to pure-strategy profiles. As a result, we no longer face the numerical precision issues encountered by the original approach, and both the resulting algorithm and its analysis are considerably simplified. Our new separation oracle can be understood as a derandomization of Papadimitriou and Roughgarden's original separation oracle via the method of conditional probabilities. Also, the equilibria returned by our algorithm are distributions with polynomial-sized supports, which are simpler (in the sense of being representable in fewer bits) than the mixtures of product distributions produced previously; no tractable algorithm has previously been proposed for identifying such equilibria.Comment: 15 page

Machine learning for discovering laws of nature

A microscopic particle obeys the principles of quantum mechanics -- so where is the sharp boundary between the macroscopic and microscopic worlds? It was this "interpretation problem" that prompted Schr\"odinger to propose his famous thought experiment (a cat that is simultaneously both dead and alive) and sparked a great debate about the quantum measurement problem, and there is still no satisfactory answer yet. This is precisely the inadequacy of rigorous mathematical models in describing the laws of nature. We propose a computational model to describe and understand the laws of nature based on Darwin's natural selection. In fact, whether it's a macro particle, a micro electron or a security, they can all be considered as an entity, the change of this entity over time can be described by a data series composed of states and values. An observer can learn from this data series to construct theories (usually consisting of functions and differential equations). We don't model with the usual functions or differential equations, but with a state Decision Tree (determines the state of an entity) and a value Function Tree (determines the distance between two points of an entity). A state Decision Tree and a value Function Tree together can reconstruct an entity's trajectory and make predictions about its future trajectory. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer's expected value. There is no differential equation in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to rediscovering Newton's law, the Born rule (quantum mechanics) and the efficient market hypothesis (financial market)

Research Brief: The Role of Tasks and Skills in Explaining the Disability Pay Gap

A disparity in pay exists between workers with and without disabilities. This gap persists even in analyses that control for a variety of factors and incorporate compensation benefits other than wages and salaries. To better understand the underlying sources of these differences, occupation-level data on employee skill and task requirements are considered. Evaluating the earnings gap with this additional information provides insights regarding the economic returns to certain workplace tasks and skills that may contribute to the earnings gap that we observe for people with disabilities

From Data Fusion to Knowledge Fusion

The task of {\em data fusion} is to identify the true values of data items (eg, the true date of birth for {\em Tom Cruise}) among multiple observed values drawn from different sources (eg, Web sites) of varying (and unknown) reliability. A recent survey\cite{LDL+12} has provided a detailed comparison of various fusion methods on Deep Web data. In this paper, we study the applicability and limitations of different fusion techniques on a more challenging problem: {\em knowledge fusion}. Knowledge fusion identifies true subject-predicate-object triples extracted by multiple information extractors from multiple information sources. These extractors perform the tasks of entity linkage and schema alignment, thus introducing an additional source of noise that is quite different from that traditionally considered in the data fusion literature, which only focuses on factual errors in the original sources. We adapt state-of-the-art data fusion techniques and apply them to a knowledge base with 1.6B unique knowledge triples extracted by 12 extractors from over 1B Web pages, which is three orders of magnitude larger than the data sets used in previous data fusion papers. We show great promise of the data fusion approaches in solving the knowledge fusion problem, and suggest interesting research directions through a detailed error analysis of the methods.Comment: VLDB'201