Optimizing the Performative Risk under Weak Convexity Assumptions
- URL: http://arxiv.org/abs/2209.00771v1
- Date: Fri, 2 Sep 2022 01:07:09 GMT
- Title: Optimizing the Performative Risk under Weak Convexity Assumptions
- Authors: Yulai Zhao
- Abstract summary: In performative prediction, a predictive model impacts the distribution that generates future data.
Prior work has identified a pair of general conditions on the loss and the mapping from model parameters to distributions that implies convexity the performative risk.
In this paper, we relax these assumptions, without sacrificing the amenability of the performative minimization risk problem for iterative optimization methods.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In performative prediction, a predictive model impacts the distribution that
generates future data, a phenomenon that is being ignored in classical
supervised learning. In this closed-loop setting, the natural measure of
performance, denoted the performative risk, captures the expected loss incurred
by a predictive model after deployment. The core difficulty of minimizing the
performative risk is that the data distribution itself depends on the model
parameters. This dependence is governed by the environment and not under the
control of the learner. As a consequence, even the choice of a convex loss
function can result in a highly non-convex performative risk minimization
problem. Prior work has identified a pair of general conditions on the loss and
the mapping from model parameters to distributions that implies convexity of
the performative risk. In this paper, we relax these assumptions and focus on
obtaining weaker notions of convexity, without sacrificing the amenability of
the performative risk minimization problem for iterative optimization methods.
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