Empirical Welfare Maximization with Constraints

Sun, Liyang

doi:10.48550/arxiv.2103.15298

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…1 See Dehejia (2005), Stoye (2009Stoye ( , 2012, Hirano andPorter (2009, 2020), Chamberlain (2011Chamberlain ( , 2020, Tetenov (2012), andChristensen et al (2022) for decision theoretic analyses of statistical treatment rules. There is also a growing literature learning on studying individualized treatment assignments including Kitagawa and Tetenov (2018), Athey and Wager (2021), Kasy and Sautmann (2021), Kitagawa et al (2021), Mbakop and Tabord-Meehan (2021), Sun (2021), and Adjaho and Christensen (2022), among others. These works do not consider settings that allow for the network spillovers of treatments.…”

Section: Literature Reviewmentioning

confidence: 99%

Individualized Treatment Allocation in Sequential Network Games

Kitagawa¹,

Wang²

2023

Preprint

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Designing individualized allocation of treatments so as to maximize the equilibrium welfare of interacting agents has many policy-relevant applications. Focusing on sequential decision games of interacting agents, this paper develops a method to obtain optimal treatment assignment rules that maximize a social welfare criterion by evaluating stationary distributions of outcomes. Stationary distributions in sequential decision games are given by Gibbs distributions, which are difficult to optimize with respect to a treatment allocation due to analytical and computational complexity. We apply a variational approximation to the stationary distribution and optimize the approximated equilibrium welfare with respect to treatment allocation using a greedy optimization algorithm. We characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. We establish the convergence rate of this bound. We demonstrate the performance of our proposed method in simulation exercises.

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Section: Literature Reviewmentioning

confidence: 99%

Individualized Treatment Allocation in Sequential Network Games

Kitagawa¹,

Wang²

2023

Preprint

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“…Other work considers resource-budgeted allocation Kube et al (2019), which is structured because of reformulation of thresholds Lopez et al (2020). Sun (2021) studies sharp asymptotics for the additional challenge of stochasticity in the budget.…”

Section: Related Workmentioning

confidence: 99%

Off-Policy Evaluation with Policy-Dependent Optimization Response

Guo¹,

Jordan²,

Zhou³

2022

Preprint

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The intersection of causal inference and machine learning for decision-making is rapidly expanding, but the default decision criterion remains an average of individual causal outcomes across a population. In practice, various operational restrictions ensure that a decision-maker's utility is not realized as an average but rather as an output of a downstream decision-making problem (such as matching, assignment, network flow, minimizing predictive risk). In this work, we develop a new framework for off-policy evaluation with a policy-dependent linear optimization response: causal outcomes introduce stochasticity in objective function coefficients. In this framework, a decision-maker's utility depends on the policy-dependent optimization, which introduces a fundamental challenge of optimization bias even for the case of policy evaluation. We construct unbiased estimators for the policy-dependent estimand by a perturbation method. We also discuss the asymptotic variance properties for a set of plug-in regression estimators adjusted to be compatible with that perturbation method. Lastly, attaining unbiased policy evaluation allows for policy optimization, and we provide a general algorithm for optimizing causal interventions. We corroborate our theoretical results with numerical simulations.

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Empirical Welfare Maximization with Constraints

Cited by 2 publications

References 15 publications

Individualized Treatment Allocation in Sequential Network Games

Individualized Treatment Allocation in Sequential Network Games

Off-Policy Evaluation with Policy-Dependent Optimization Response

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