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• W3204249879 abstract "This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the learner's and agent's previous states. The said samples are used by the learner to optimize a loss function. This closed loop algorithm is studied as a state-dependent stochastic approximation (SA) algorithm, where we show that it finds a fixed point known as the performative stable solution. Our setting models the unforgetful nature and the reliance on past experiences of agent(s). Our contributions are three-fold. First, we demonstrate that the SA algorithm can be modeled with biased stochastic gradients driven by a controlled Markov chain (MC) whose transition probability is adapted to the learner's state. Second, we present a novel finite-time performance analysis of the state-dependent SA algorithm. We show that the expected squared distance to the performative stable solution decreases as ${cal O}(1/k)$, where $k$ is the iteration number. Third, numerical experiments are conducted to verify our findings." @default.
• W3204249879 created "2021-10-11" @default.
• W3204249879 creator A5055166851 @default.
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• W3204249879 date "2021-10-02" @default.
• W3204249879 modified "2023-09-26" @default.
• W3204249879 title "State Dependent Performative Prediction with Stochastic Approximation" @default.
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• W3204249879 doi "https://doi.org/10.48550/arxiv.2110.00800" @default.
• W3204249879 hasPublicationYear "2021" @default.
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