Map estimation for Bayesian mixture models with submodular priors

Halabi, Marwa El; Baldassarre, Luca; Cevher, Volkan

doi:10.1109/mlsp.2014.6958846

Cited by 1 publication

(1 citation statement)

References 30 publications

(26 reference statements)

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“…Given this, there is considerable interest in solving non-submodular optimization problems using greedy algorithms amongst researchers. See Das and Kempe (2011), Bian et al (2017), El Halabi and Jegelka (2020), and Jagalur-Mohan and Marzouk (2021. We use the result from Bian et al (2017) to produce a performance guarantee for our treatment allocation problem by clarifying sufficient conditions for obtaining non-trivial bounds on the submodularity ratio and the curvature of our objective function.…”

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%