11 research outputs found
Mechanism Design via Dantzig-Wolfe Decomposition
In random allocation rules, typically first an optimal fractional point is
calculated via solving a linear program. The calculated point represents a
fractional assignment of objects or more generally packages of objects to
agents. In order to implement an expected assignment, the mechanism designer
must decompose the fractional point into integer solutions, each satisfying
underlying constraints. The resulting convex combination can then be viewed as
a probability distribution over feasible assignments out of which a random
assignment can be sampled. This approach has been successfully employed in
combinatorial optimization as well as mechanism design with or without money.
In this paper, we show that both finding the optimal fractional point as well
as its decomposition into integer solutions can be done at once. We propose an
appropriate linear program which provides the desired solution. We show that
the linear program can be solved via Dantzig-Wolfe decomposition. Dantzig-Wolfe
decomposition is a direct implementation of the revised simplex method which is
well known to be highly efficient in practice. We also show how to use the
Benders decomposition as an alternative method to solve the problem. The
proposed method can also find a decomposition into integer solutions when the
fractional point is readily present perhaps as an outcome of other algorithms
rather than linear programming. The resulting convex decomposition in this case
is tight in terms of the number of integer points according to the
Carath{\'e}odory's theorem
A Truthful Mechanism for the Generalized Assignment Problem
We propose a truthful-in-expectation, -approximation mechanism for a
strategic variant of the generalized assignment problem (GAP). In GAP, a set of
items has to be optimally assigned to a set of bins without exceeding the
capacity of any singular bin. In the strategic variant of the problem we study,
values for assigning items to bins are the private information of bidders and
the mechanism should provide bidders with incentives to truthfully report their
values. The approximation ratio of the mechanism is a significant improvement
over the approximation ratio of the existing truthful mechanism for GAP.
The proposed mechanism comprises a novel convex optimization program as the
allocation rule as well as an appropriate payment rule. To implement the convex
program in polynomial time, we propose a fractional local search algorithm
which approximates the optimal solution within an arbitrarily small error
leading to an approximately truthful-in-expectation mechanism. The presented
algorithm improves upon the existing optimization algorithms for GAP in terms
of simplicity and runtime while the approximation ratio closely matches the
best approximation ratio given for GAP when all inputs are publicly known.Comment: 18 pages, Earlier version accepted at WINE 201
Fast Convex Decomposition for Truthful Social Welfare Approximation
Approximating the optimal social welfare while preserving truthfulness is a
well studied problem in algorithmic mechanism design. Assuming that the social
welfare of a given mechanism design problem can be optimized by an integer
program whose integrality gap is at most , Lavi and Swamy~\cite{Lavi11}
propose a general approach to designing a randomized -approximation
mechanism which is truthful in expectation. Their method is based on
decomposing an optimal solution for the relaxed linear program into a convex
combination of integer solutions. Unfortunately, Lavi and Swamy's decomposition
technique relies heavily on the ellipsoid method, which is notorious for its
poor practical performance. To overcome this problem, we present an alternative
decomposition technique which yields an approximation
and only requires a quadratic number of calls to an integrality gap verifier
Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021
BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed
Recommended from our members
Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021
Background
Disorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.
Methods
We estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.
Findings
Globally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.
Interpretation
As the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed.
Funding
Bill & Melinda Gates Foundation
A truthful-in-expectation mechanism for the generalized assignment problem
Abstract. We propose a truthful-in-expectation, (1 − 1 e )-approximation mechanism for the generalized assignment auction. In such an auction, each bidder has a knapsack valuation function and bidders' values for items are private. We present a novel convex optimization program for the auction which results in a maximal-in-distributional-range (MIDR) allocation rule. The presented program contains at least a (1 − 1 e ) ratio of the optimal social welfare. We show how to implement the convex program in polynomial time using a fractional local search algorithm which approximates the optimal solution within an arbitrarily small error. This leads to an approximately MIDR allocation rule which in turn can be transformed to an approximately truthful-in-expectation mechanism. Our contribution has algorithmic importance, as well; it simplifies the existing optimization algorithms for the GAP while the approximation ratio is comparable to the best given approximation