Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure

The Need for a Different Approach to Financial Reporting and Standard-setting

International Financial Reporting Standards are questioned. Possibly, there is a need for a different kind of standards and a different procedure for developing them. No doubt, there is a need for a more profound theoretical approach to these issues. Theory-building in accounting should include approaches whereby problem descriptions have a broad coverage and cross the boarders of traditional specialisations. In this paper, a theoretical approach is outlined. According to this approach, insights into control problems for every organisation and system can be gained by analysing relationships between global value chains and a hierarchy of one or several organisations. Time is crucial. Instrumentality is regarded as an inevitable and necessary guide line for any control system that relates resources to functions and visions. Instrumentality concerns the effects of tools on certain functions. In the paper financial reporting and standard-setting are placed in a wide context in which longitudinal relationships are essential for individuals, organisations and control systems. Basic financial accounting concepts and their relationships with business events are discussed. The importance of uncertainty for financial reporting is emphasized, and so is the fact, that control from top-levels is exercised at a distance. A tendency to instrumentalism is also recognized: measures and procedures, for example standard setting procedures, tend to be important in themselves, irrespective of ultimate economic functions in a wider perspective. The analysis in the paper is one application of a general approach to financial control for all types of organisations. The general approach is based on a number of previous research-oriented books published over several decades and the author´s specific own experiences from internal and external processes with organisations in focus. Consistency and integrative power of the ideas have been tested in relation to certain books in various fields outside the core of the subject: applied systems theory, theatre, sociology, economic history, institutional theory and economics.financial reporting; International Financial Reporting Standards; standard-setting; accounting standard setting bodies; supervisory boards; corporate governance; transparency; market value accounting; mark-to-market; fair values; historical values; accounting theory.

Towards a General Theory of Financial Control for Organisations

In this paper, a theory of accounting, control and accounting-related areas is outlined.It is based on a number of previous research-oriented books published over several decades and the author´s specific own experiences from internal and external processes with organisations in focus.Consistency and integrative power of the ideas have been tested in relation to certain books in various fields outside the core of the subject:theatre,sociology, applied systems theory,economic history, institutional theory and economics.The general approach can be described in simple terms as follows.There are global value chains, from resources to output that are in use.These chains change with time.Uncertainty and unpredictability prevail for the present state and for possible changes; to some extent it is possible to estimate risks of the future. At any moment, each organisation has taken some limited position on a chain.Each organisation has a hierarchy which lies above operations. Over time, chains, organisations, hierarchies, output and personal functions vary. According to the approach, insights into control problems for every organisation and system can be gained by analysing relationships between global value chains and a hierarchy of one or several organisations.Time is crucial.financial control; management control; public administration; financial entities; financial reporting; dependencies; function-driven organisations; pay-driven organisations; transfer-driven organisations; supervisory boards; mass media; auditors; natural systems; panarchy; pseudo-commercial units; inter-organisational control; long-term control; short-term effects; hierarchies; global value chains; vertical control; horizontal control; corporate governance; remote control; controllability; transparency; values-in-use; values-in-exchange; fair values; historical costing; opportunity costs; product costing; transfer pricing; local optimization; time-bound optimization; longitudinal relationships.

EUROnu-WP6 2010 Report

This is a summary of the work done by the Working Package 6 (Physics) of the EU project "EUROnu" during the second year of activity of the project.Comment: 82 pages, 51 eps figure

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR

The Role of Classification in Knowledge Represantation and Discovery

The link between classification and knowledge is explored. Classification schemes have properties that enable the representation of entities and relationships in structures that reflect knowledge of the domain being classified. The strengths and limitations of four classificatory approaches are described in terms of their ability to reflect, discover, and create new knowledge. These approaches are hierarchies, trees, paradigms, and faceted analysis. Examples are provided of the way in which knowledge and the classification process affect each other