Two-timescale Derivative Free Optimization for Performative Prediction with Markovian Data
This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in strategic classification. We consider a state-dependent set...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
09.10.2023
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Subjects | |
Online Access | Get full text |
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Summary: | This paper studies the performative prediction problem where a learner aims
to minimize the expected loss with a decision-dependent data distribution. Such
setting is motivated when outcomes can be affected by the prediction model,
e.g., in strategic classification. We consider a state-dependent setting where
the data distribution evolves according to an underlying controlled Markov
chain. We focus on stochastic derivative free optimization (DFO) where the
learner is given access to a loss function evaluation oracle with the above
Markovian data. We propose a two-timescale DFO($\lambda$) algorithm that
features (i) a sample accumulation mechanism that utilizes every observed
sample to estimate the overall gradient of performative risk, and (ii) a
two-timescale diminishing step size that balances the rates of DFO updates and
bias reduction. Under a general non-convex optimization setting, we show that
DFO($\lambda$) requires ${\cal O}( 1 /\epsilon^3)$ samples (up to a log factor)
to attain a near-stationary solution with expected squared gradient norm less
than $\epsilon > 0$. Numerical experiments verify our analysis. |
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DOI: | 10.48550/arxiv.2310.05792 |