scholarly journals Shape-Constrained Estimation of Value Functions

2013 ◽  
Author(s):  
Mohammad Mousavi ◽  
Peter W. Glynn
Keyword(s):  
Value Functions ◽  
Constrained Estimation ◽  
Shape Constrained Estimation

scholarly journals Uncoupled isotonic regression via minimum Wasserstein deconvolution

2019 ◽  
Vol 8 (4) ◽  
pp. 691-717 ◽  
Author(s):  
Philippe Rigollet ◽  
Jonathan Weed
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Regression Function ◽  
Isotonic Regression ◽  
Upper And Lower Bounds ◽  
Constrained Estimation ◽  
Standard Problem ◽  
Minimax Rates ◽  
Shape Constrained Estimation ◽  
Optimal Transport Theory

Abstract Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown non-decreasing regression function $f$ from independent pairs $(x_i, y_i)$ where ${\mathbb{E}}[y_i]=f(x_i), i=1, \ldots n$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart, where one is given only the unordered sets $\{x_1, \ldots , x_n\}$ and $\{y_1, \ldots , y_n\}$. In this work, we leverage tools from optimal transport theory to derive minimax rates under weak moments conditions on $y_i$ and to give an efficient algorithm achieving optimal rates. Both upper and lower bounds employ moment-matching arguments that are also pertinent to learning mixtures of distributions and deconvolution.

The Received Wisdom

2018 ◽  
Author(s):  
Meghan Sullivan
Keyword(s):  
Temporal Discounting ◽  
Value Functions ◽  
Distant Future ◽  
Rational Planning ◽  
Future Discounting ◽  
The Future

This chapter introduces the reader to future discounting and some received wisdom. The received wisdom about rational planning tends to assume that it is irrational to have near‐biased preferences (i.e., preferences for lesser goods now compared to greater goods further in the future).Thechapter describes these preferences by introducing the reader to value functions. Value functions are then used to model different kinds of distant future temporal discounting (e.g., hyperbolic, exponential, absolute). Finally, the chapter makes a distinction between temporal discounting and risk discounting. It offers a reverse lottery test to tease apart these two kinds of discounting.

Value functions and two classes of binary codes

2021 ◽  
Vol 344 (3) ◽  
pp. 112261
Author(s):  
Zihui Liu
Keyword(s):  
Binary Codes ◽  
Value Functions

scholarly journals Assessing the Performance of Interactive Multiobjective Optimization Methods

2021 ◽  
Vol 54 (4) ◽  
pp. 1-27
Author(s):  
Bekir Afsar ◽  
Kaisa Miettinen ◽  
Francisco Ruiz
Keyword(s):  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Interactive Methods ◽  
Value Functions ◽  
Technical Aspects ◽  
Preference Information ◽  
Multiobjective Optimization Problems ◽  
Human Decision

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed.

Linearly constrained estimation by mathematical programming

1989 ◽  
Vol 42 (3) ◽  
pp. 254-267 ◽  
Author(s):  
Emil Klafszky ◽  
Jànos Mayer ◽  
Tamás Terlaky
Keyword(s):  
Mathematical Programming ◽  
Constrained Estimation ◽  
Linearly Constrained

scholarly journals Sensitivity Analysis for Two-Level Value Functions with Applications to Bilevel Programming

2012 ◽  
Vol 22 (4) ◽  
pp. 1309-1343 ◽  
Author(s):  
S. Dempe ◽  
B. S. Mordukhovich ◽  
A. B. Zemkoho
Keyword(s):  
Sensitivity Analysis ◽  
Bilevel Programming ◽  
Value Functions
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