A small estimated Euro area model with rational expectations and nominal rigidities

In this paper we estimate a small model of the euro area to be used as a laboratory for evaluating the performance of alternative monetary policy strategies. We start with the relationship between output and inflation and investigate the fit of the nominal wage contracting model due to Taylor (1980)and three different versions of the relative real wage contracting model proposed by Buiter and Jewitt (1981)and estimated by Fuhrer and Moore (1995a) for the United States. While Fuhrer and Moore reject the nominal contracting model in favor of the relative contracting model which induces more inflation persistence, we find that both models fit euro area data reasonably well. When considering France, Germany and Italy separately, however, we find that the nominal contracting model fits German data better, while the relative contracting model does quite well in countries which transitioned out of a high inflation regime such as France and Italy. We close the model by estimating an aggregate demand relationship and investigate the consequences of the different wage contracting specifications for the inflation-output variability tradeoff, when interest rates are set according to Taylor 's rule

Unconventional Cosmology

I review two cosmological paradigms which are alternative to the current inflationary scenario. The first alternative is the "matter bounce", a non-singular bouncing cosmology with a matter-dominated phase of contraction. The second is an "emergent" scenario, which can be implemented in the context of "string gas cosmology". I will compare these scenarios with the inflationary one and demonstrate that all three lead to an approximately scale-invariant spectrum of cosmological perturbations.Comment: 45 pages, 10 figures; invited lectures at the 6th Aegean Summer School "Quantum Gravity and Quantum Cosmology", Chora, Naxos, Greece, Sept. 12 - 17 2012, to be publ. in the proceedings; these lecture notes form an updated version of arXiv:1003.1745 and arXiv:1103.227

Statistical Learning Theory for Control: A Finite Sample Perspective

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions.Comment: Survey Paper, Submitted to Control Systems Magazine. Second version contains additional motivation for finite sample statistics and more detailed comparison with classical literatur

A Small Estimated Euro Area Model with Rational Expectations and Nominal Rigidities

In this paper we estimate a small model of the euro area to be used as a laboratory for evaluating the performance of alternative monetary policy strategies. We start with the relationship between output and inflation and investigate the fit of the nominal wage contracting model due to Taylor (1980)and three different versions of the relative real wage contracting model proposed by Buiter and Jewitt (1981)and estimated by Fuhrer and Moore (1995a) for the United States. While Fuhrer and Moore reject the nominal contracting model in favor of the relative contracting model which induces more inflation persistence, we find that both models fit euro area data reasonably well. When considering France, Germany and Italy separately, however, we find that the nominal contracting model fits German data better, while the relative contracting model does quite well in countries which transitioned out of a high inflation regime such as France and Italy. We close the model by estimating an aggregate demand relationship and investigate the consequences of the different wage contracting specifications for the inflation-output variability tradeoff, when interest rates are set according to Taylor ’s rule.European Monetary Union, euro area, macroeconomic modelling, rational expectations, nominal rigidities, overlapping wage contracts, inflation persistence, monetary policy rules

Effective offline training and efficient online adaptation

Developing agents that behave intelligently in the world is an open challenge in machine learning. Desiderata for such agents are efficient exploration, maximizing long term utility, and the ability to effectively leverage prior data to solve new tasks. Reinforcement learning (RL) is an approach that is predicated on learning by directly interacting with an environment through trial-and-error, and presents a way for us to train and deploy such agents. Moreover, combining RL with powerful neural network function approximators – a sub-field known as “deep RL” – has shown evidence towards achieving this goal. For instance, deep RL has yielded agents that can play Go at superhuman levels, improve the efficiency of microchip designs, and learn complex novel strategies for controlling nuclear fusion reactions. A key issue that stands in the way of deploying deep RL is poor sample efficiency. Concretely, while it is possible to train effective agents using deep RL, the key successes have largely been in environments where we have access to large amounts of online interaction, often through the use of simulators. However, in many real-world problems, we are confronted with scenarios where samples are expensive to obtain. As has been alluded to, one way to alleviate this issue is through accessing some prior data, often termed “offline data”, which can accelerate how quickly we learn such agents, such as leveraging exploratory data to prevent redundant deployments, or using human-expert data to quickly guide agents towards promising behaviors and beyond. However, the best way to incorporate this data into existing deep RL algorithms is not straightforward; naïvely pre-training using RL algorithms on this offline data, a paradigm called “offline RL” as a starting point for subsequent learning is often detrimental. Moreover, it is unclear how to explicitly derive useful behaviors online that are positively influenced by this offline pre-training. With these factors in mind, this thesis follows a 3-pronged strategy towards improving sample-efficiency in deep RL. First, we investigate effective pre-training on offline data. Then, we tackle the online problem, looking at efficient adaptation to environments when operating purely online. Finally, we conclude with hybrid strategies that use offline data to explicitly augment policies when acting online

Recurrent Linear Transformers

The self-attention mechanism in the transformer architecture is capable of capturing long-range dependencies and it is the main reason behind its effectiveness in processing sequential data. Nevertheless, despite their success, transformers have two significant drawbacks that still limit their broader applicability: (1) In order to remember past information, the self-attention mechanism requires access to the whole history to be provided as context. (2) The inference cost in transformers is expensive. In this paper we introduce recurrent alternatives to the transformer self-attention mechanism that offer a context-independent inference cost, leverage long-range dependencies effectively, and perform well in practice. We evaluate our approaches in reinforcement learning problems where the aforementioned computational limitations make the application of transformers nearly infeasible. We quantify the impact of the different components of our architecture in a diagnostic environment and assess performance gains in 2D and 3D pixel-based partially-observable environments. When compared to a state-of-the-art architecture, GTrXL, inference in our approach is at least 40% cheaper while reducing memory use in more than 50%. Our approach either performs similarly or better than GTrXL, improving more than 37% upon GTrXL performance on harder tasks.Comment: transformers, reinforcement learning, partial observabilit

Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.MSMT-7778/2014, FEDER, European Regional Development Fund; LO1303, FEDER, European Regional Development Fund; CZ.1.05/2.1.00/19.0376, FEDER, European Regional Development FundEuropean Regional Development Fund through the Project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; National Sustainability Program Project [LO1303 (MSMT-7778/2014)

Cosmology of the Very Early Universe

In these lectures I focus on early universe models which can explain the currently observed structure on large scales. I begin with a survey of inflationary cosmology, the current paradigm for understanding the origin of the universe as we observe it today. I will discuss some progress and problems in inflationary cosmology before moving on to a description of two alternative scenarios - the Matter Bounce and String Gas Cosmology. All early universe models connect to observations via the evolution of cosmological perturbations - a topic which will be discussed in detail in these lectures.Comment: 38 pages, 15 figures, to be published in the proceedings of the XIV Special Course in Astronomy, Observatorio Nacional, Brazi