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# System prepended metadata

title: Optimal Stopping

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# Optimal Stopping

## Prophet Inequality

* Prophets and Secretaries http://www.cs.cmu.edu/~anupamg/ipco17/ipco-talk3.pdf

* Recent Developments in Prophet Inequalities https://www.dii.uchile.cl/~jcorrea/papers/Journals/CFHOV2019.pdf
* Prophet secretary (arrive in random order) https://arxiv.org/pdf/1507.01155.pdf

## Secretary problem

* A Knapsack Secretary Problem with Applications http://people.csail.mit.edu/nickle/pubs/knapsackSecretary.pdf

* The Noisy Secretary Problem and Some Results on Extreme Concomitant Variables https://repository.upenn.edu/cgi/viewcontent.cgi?article=1601&context=statistics_papers

## Hiring Problem

* The Hiring Problem and Lake Wobegon Strategies http://theory.stanford.edu/~sergei/papers/hiring-soda.pdf

* The Hiring Problem: An Analytic and Experimental Study (A. Helmi thesis) https://www.researchgate.net/publication/42366403_The_Hiring_Problem_An_Analytic_and_Experimental_Study

## Knapsack Problem

* The Dynamic and Stochastic Knapsack Problem with Deadlines (values are known) https://www.jstor.org/stable/2634548?seq=1

* Revenue Maximization in the Dynamic Knapsack
Problem http://pluto.huji.ac.il/~alexg/pdf/knapsack.pdf

* Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons  https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/3943/vanryzin_optimal_dynamic_pricing.pdf

# Covariate Shift

* List of cognitive biases https://en.wikipedia.org/wiki/List_of_cognitive_biases

* Data Shift in ML (book) http://www.acad.bg/ebook/ml/The.MIT.Press.Dataset.Shift.in.Machine.Learning.Feb.2009.eBook-DDU.pdf

* Machine Learning in Non-stationary Environments (book)

* Improving predictive inference under covariate shift by weighting the log-likelihood function https://www.researchgate.net/publication/230710850_Improving_predictive_inference_under_covariate_shift_by_weighting_the_log-likelihood_function

* Maximum likelihood estimation of misspecified models http://www.sungpark.net/White_IMtest.pdf

* SELECTION BIAS IN LINEAR REGRESSION, LOGIT AND PROBIT MODELS https://authors.library.caltech.edu/81145/1/sswp698.pdf

* How do you correct selection bias ? https://medium.com/@akelleh/how-do-you-correct-selection-bias-d781a9b12de2

* Sample Selection Bias Correction Theory https://cs.nyu.edu/~mohri/pub/bias.pdf


* Mixture Regression for Covariate Shift http://papers.nips.cc/paper/3019-mixture-regression-for-covariate-shift.pdf

# Learning under Ambiguity


* AMBIGUITY, INFORMATION QUALITY AND ASSET PRICING https://core.ac.uk/download/pdf/7081046.pdf

* Recursive Multiple Priors http://people.bu.edu/lepstein/files-research/rectang50.pdf

* AMBIGUITY AND ASSET MARKETS https://www.nber.org/papers/w16181

* LEARNING UNDER AMBIGUITY http://hassler-j.iies.su.se/COURSES/NewPrefs/Papers/Ambiguity/EpsteinSchneider%20ambig%20May%2004.pdf

* Ambiguity Aversion in Ellsberg Frameworks
 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2294514
 
 # Expected Utility Theory
 
 * On the Efficiency of Competitive Stock Markets Where Trades Have Diverse Information https://www.jstor.org/stable/2326627?seq=1

* Does ambiguity aversion reinforce risk aversion? Applications to portfolio choices and asset prices http://fdir.idei.fr/wp-content/uploads/2011/gt1/gollier_ambiguity.pdf
* Choice under Uncertainty https://web.stanford.edu/~jdlevin/Econ%20202/Uncertainty.pdf
* Choice Under Uncertainty: Problems Solved and Unsolved
http://econ.ucsb.edu/~oprea/176/Choice.pdf


# Statistical Discrimination

* Theory of statistical discimination: a survey https://www.nber.org/papers/w15860.pdf
* Lecture Note: The Economics of Discrimination — Theory https://economics.mit.edu/files/553
* Will Affirmative-Action Policies Eliminate Negative Stereotypes? https://inequality.stanford.edu/sites/default/files/media/_media/pdf/Reference%20Media/Coate%20and%20Loury_1993_Discrimination%20and%20Prejudice.pdf


# Ingroup Favoritism, Outgroup  homogeneity

* https://en.wikipedia.org/wiki/In-group_favoritism
* https://en.wikipedia.org/wiki/Out-group_homogeneity
* Implicit Bias. https://plato.stanford.edu/entries/implicit-bias/
* Perceived distributions of the characteristics of in-group and out-group members: Empirical evidence and a computer simulation https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.57.2.165 
*. https://www2.psych.ubc.ca/~schaller/Psyc590Readings/RubinBadea2012.pdf

* https://cogsci.mindmodeling.org/2017/papers/0139/paper0139.pdf


# Fairness in Multistage Decisions-Making

* Fair pipelines https://arxiv.org/pdf/1707.00391.pdf
> Study how fairness propagates through two-stage pipeline. Show that an approximate equal opportunity is multiplicative, i.e. if first stage satisfies (1+e)-equal opportunity and second stage (1+d)-equal opportunity, then the whole pipeline satisfies (1+e)(1+d)-equal opporunity.
>


* Downstream Effects of Affirmative Action https://arxiv.org/pdf/1808.09004.pdf

> A two-stage college admission and hiring is considered. The authors study if certain fair policies—irrelevance of group membership (*rational employers selecting employees from the college population should not make hiring decisions based on group membership*) and equal opportunity (*the probability that an individual is accepted to college and then ultimately hired by an employer may depend on an individual’s type, but conditioned on
their type, should not depend on their demographic group*) — can be satisfied. They show that it is possible to satisfy both if the college grades are not reported to the employer, but there are settings where these fairness conditions cannot be satisfied even in isolation.


* Delayed impact of fair machine learning https://arxiv.org/pdf/1803.04383.pdf



* Fairness under composition https://arxiv.org/pdf/1806.06122.pdf
> Investigate how fairness works under compositions, i.e. if have multiple individually fair decisions how they compose if they are aggregate as OR/AND relations.
> 
* A Short-term Intervention for Long-term Fairness in the Labor Market https://arxiv.org/pdf/1712.00064.pdf
>ss
>

* Pipeline Interventions https://arxiv.org/pdf/2002.06592.pdf
> Propose a model based on directed acyclic graph, where each starting node represents a certain group, transition from layer to layer depicts transition between social steps. Consider two cases of how to adjust transitions given fix budget to maximize (a) social welfare; (b) minimal welfare. They solve the optimization problem using DP approach and define a price of fairness as a relaitve utilities of OPT_{sf} / OPT_{maximin} and show its bounds.
 
* Individual fairness in pipelines https://arxiv.org/pdf/2004.05167v1.pdf



