Near unanimity: an obstacle to general duality theory

1995 ◽  
Vol 33 (3) ◽  
pp. 428-439 ◽  
Author(s):  
B. A. Davey ◽  
L. Heindorf ◽  
R. McKenzie
Keyword(s):  
Duality Theory ◽  
Near Unanimity ◽  
General Duality ◽  
General Duality Theory

scholarly journals Duality in finite dimensional complex space

1978 ◽  
Vol 18 (1) ◽  
pp. 65-75
Author(s):  
C.H. Scott ◽  
T.R. Jefferson
Keyword(s):  
Quadratic Programming ◽  
Duality Theory ◽  
Complex Space ◽  
Optimization Problems ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Mathematical Programs ◽  
Finite Dimensional ◽  
General Duality ◽  
General Duality Theory

The idea of duality is now a widely accepted and useful idea in the analysis of optimization problems posed in real finite dimensional vector spaces. Although similar ideas have filtered over to the analysis of optimization problems in complex space, these have mainly been concerned with problems of the linear and quadratic programming variety. In this paper we present a general duality theory for convex mathematical programs in finite dimensional complex space, and, by means of an example, show that this formulation captures all previous results in the area.

scholarly journals A GENERAL DUALITY THEORY FOR CLONES

2013 ◽  
Vol 23 (03) ◽  
pp. 457-502 ◽  
Author(s):  
SEBASTIAN KERKHOFF
Keyword(s):  
Duality Theory ◽  
The Relationship ◽  
General Duality ◽  
General Duality Theory

Inspired by work of Mašulović, we outline a general duality theory for clones that will allow us to dualize any given clone, together with its relational counterpart and the relationship between them. Afterwards, we put the approach to work and illustrate it by producing some specific results for concrete examples as well as some general results that come from studying the duals of clones in a rather abstract fashion.

Informed Consent and the Elusive Dichotomy Between Standard and Experimental Therapy

2002 ◽  
Vol 28 (4) ◽  
pp. 361-408
Author(s):  
Lars Noah
Keyword(s):  
Clinical Trials ◽  
Informed Consent ◽  
Patient Autonomy ◽  
College Campuses ◽  
Human Experimentation ◽  
Experimental Therapy ◽  
Academic Literature ◽  
Medical Experimentation ◽  
Disclosure Rules ◽  
Near Unanimity

A rich academic literature exists about issues of informed consent in medical care, and, to a lesser extent, about a variety of issues posed by human experimentation. Most commentators regard patient autonomy as a desirable— though in practice often unattainable—goal, and near unanimity exists about the necessity for even fuller disclosure before experimenting on subjects. Although this Article intentionally side-steps the broader debate about informed consent, it challenges the conventional wisdom that special disclosure rules should apply in the experimental context.Clinical trials have become big business. Estimates suggest that as many as twenty million Americans have enrolled in formal biomedical studies, though, as a measure of the full scope of medical experimentation on humans, that figure may represent only the proverbial tip of the iceberg. Historically, sponsors of clinical trials recruited subjects informally, counting on word of mouth among physicians and also perhaps posting flyers around college campuses.

scholarly journals Fully distributed actor-critic architecture for multitask deep reinforcement learning

2021 ◽  
Vol 36 ◽  
Author(s):  
Sergio Valcarcel Macua ◽  
Ian Davies ◽  
Aleksi Tukiainen ◽  
Enrique Munoz de Cote
Keyword(s):  
Neural Network ◽  
Reinforcement Learning ◽  
Duality Theory ◽  
Deep Neural Network ◽  
Original Problem ◽  
Almost Sure Convergence ◽  
Continuous Control ◽  
Access Data ◽  
Central Station ◽  
Common Policy

Abstract We propose a fully distributed actor-critic architecture, named diffusion-distributed-actor-critic Diff-DAC, with application to multitask reinforcement learning (MRL). During the learning process, agents communicate their value and policy parameters to their neighbours, diffusing the information across a network of agents with no need for a central station. Each agent can only access data from its local task, but aims to learn a common policy that performs well for the whole set of tasks. The architecture is scalable, since the computational and communication cost per agent depends on the number of neighbours rather than the overall number of agents. We derive Diff-DAC from duality theory and provide novel insights into the actor-critic framework, showing that it is actually an instance of the dual-ascent method. We prove almost sure convergence of Diff-DAC to a common policy under general assumptions that hold even for deep neural network approximations. For more restrictive assumptions, we also prove that this common policy is a stationary point of an approximation of the original problem. Numerical results on multitask extensions of common continuous control benchmarks demonstrate that Diff-DAC stabilises learning and has a regularising effect that induces higher performance and better generalisation properties than previous architectures.

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