Performative Prediction with Bandit Feedback: Learning through
Reparameterization
- URL: http://arxiv.org/abs/2305.01094v3
- Date: Tue, 24 Oct 2023 20:16:24 GMT
- Title: Performative Prediction with Bandit Feedback: Learning through
Reparameterization
- Authors: Yatong Chen, Wei Tang, Chien-Ju Ho, Yang Liu
- Abstract summary: We develop a framework that reparametrizes the performative prediction as a function of the induced data distribution.
We provide a regret bound that is sublinear in the total number of performative samples taken and is only in the dimension of the model parameter.
On the application side, we believe our method is useful for large online recommendation systems like YouTube or TokTok.
- Score: 25.169419772432796
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Performative prediction, as introduced by
\citeauthor{perdomo2020performative}, is a framework for studying social
prediction in which the data distribution itself changes in response to the
deployment of a model. Existing work in this field usually hinges on three
assumptions that are easily violated in practice: that the performative risk is
convex over the deployed model, that the mapping from the model to the data
distribution is known to the model designer in advance, and the first-order
information of the performative risk is available. In this paper, we initiate
the study of performative prediction problems that do not require these
assumptions. Specifically, we develop a {\em reparameterization} framework that
reparametrizes the performative prediction objective as a function of the
induced data distribution. We also develop a two-level zeroth-order
optimization procedure, where the first level performs iterative optimization
on the distribution parameter space, and the second level learns the model that
induced a particular target distribution parameter at each iteration. Under
mild conditions, this reparameterization allows us to transform the non-convex
objective into a convex one and achieve provable regret guarantees. In
particular, we provide a regret bound that is sublinear in the total number of
performative samples taken and is only polynomial in the dimension of the model
parameter. On the application side, we believe our method is useful for large
online recommendation systems like YouTube or TikTok, where the recommendation
update frequency is high and might potentially reshape future preferences.
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