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MODEL SELECTION FOR TREATMENT CHOICE
This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model-selection using a “holdout” procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.
Journal Article
POLICY LEARNING WITH OBSERVATIONAL DATA
In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our method can be used to optimize either binary treatments or infinitesimal nudges to continuous treatments, and can leverage observational data where causal effects are identified using a variety of strategies, including selection on observables and instrumental variables. Given a doubly robust estimator of the causal effect of assigning everyone to treatment, we develop an algorithm for choosing whom to treat, and establish strong guarantees for the asymptotic utilitarian regret of the resulting policy.
Journal Article
This must be the place
Meet Daniel Sullivan, a man with a complicated life. A New Yorker living in the wilds of Ireland, he has children he never sees in California, a father he loathes in Brooklyn and a wife, Claudette, who is a reclusive ex-film star given to shooting at anyone who ventures up their driveway. He is also about to find out something about a woman he lost touch with twenty years ago, and this discovery will send him off-course, far away from wife and home. Will his love for Claudette be enough to bring him back?
Book
Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium
In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may compete in such sequential auctions in the presence of uncertainty about future bidding opportunities and competition. We formulate this problem as a sequential game of incomplete information, in which bidders know neither their own valuation distribution nor the budgets and valuation distributions of their competitors. We introduce a family of practical bidding strategies we refer to as
adaptive pacing
strategies, in which advertisers adjust their bids according to the sample path of expenditures they exhibit, and analyze the performance of these strategies in different competitive settings. We establish the asymptotic optimality of these strategies when competitors’ bids are independent and identically distributed over auctions, but also when competing bids are arbitrary. When all the bidders adopt these strategies, we establish the convergence of the induced dynamics and characterize a regime (well motivated in the context of online advertising markets) under which these strategies constitute an approximate Nash equilibrium in dynamic strategies: the benefit from unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow approximate equilibrium bidding strategies that also ensure the best performance that can be guaranteed off equilibrium.
This paper was accepted by Noah Gans, stochastic models and simulation.
Journal Article
Susannah's garden
\"When Susannah Nelson turned eighteen, she said goodbye to her boyfriend, Jake--and never saw him again. She never saw her brother again, either. Doug died in a car accident that same year. Now, at fifty, she finds herself regretting the paths not taken. Long married, a mother and a teacher, she should be happy. But she feels there's something missing in her life, although she doesn't know exactly what. Not only that, she's balancing the demands of an aging mother and a temperamental twenty-year-old daughter\"--Amazon.com.
Book
Consensus-Based Linguistic Distribution Large-Scale Group Decision Making Using Statistical Inference and Regret Theory
Large-scale group decision-making (LSGDM) deals with complex decision- making problems which involve a large number of decision makers (DMs). Such a complex scenario leads to uncertain contexts in which DMs elicit their knowledge using linguistic information that can be modelled using different representations. However, current processes for solving LSGDM problems commonly neglect a key concept in many real-world decision-making problems, such as DMs’ regret aversion psychological behavior. Therefore, this paper introduces a novel consensus based linguistic distribution LSGDM (CLDLSGDM) approach based on a statistical inference principle that considers DMs’ regret aversion psychological characteristics using regret theory and which aims at obtaining agreed solutions. Specifically, the CLDLSGDM approach applies the statistical inference principle to the consensual information obtained in the consensus process, in order to derive the weights of DMs and attributes using the consensus matrix and adjusted decision-making matrices to solve the decision-making problem. Afterwards, by using regret theory, the comprehensive perceived utility values of alternatives are derived and their ranking determined. Finally, a performance evaluation of public hospitals in China is given as an example in order to illustrate the implementation of the designed method. The stability and advantages of the designed method are analyzed by a sensitivity and a comparative analysis.
Journal Article
The stolen child : a novel
Haunted by a decision he made as a young soldier in World War I, involving a French artist and her baby, Nick Burns, with only months left to live, enlists Jenny, a college dropout, to help him unravel the mystery, forcing them both to reckon with regret, betrayal and the lives they've left behind.
BOOK
Regret theory and risk attitudes
We examine risk attitudes under regret theory and derive analytical expressions for two components—the resolution and regret premiums—of the risk premium under regret theory. We posit that regret-averse decision makers are risk seeking (resp., risk averse) for low (resp., high) probabilities of gains and that feedback concerning the foregone option reinforces risk attitudes. We test these hypotheses experimentally and estimate empirically both the resolution premium and the regret premium. Our results confirm the predominance of regret aversion but not the risk attitudes predicted by regret theory; they also clarify how feedback affects attitudes toward both risk and regret.
Journal Article