Performative Prediction

Perdomo, Juan C.; Zrnic, Tijana; Mendler-Dünner, Celestine; Hardt, Moritz

doi:10.48550/arxiv.2002.06673

Cited by 7 publications

(19 citation statements)

References 20 publications

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“…For this reason, we focus on the problem of making online control decisions u k such that, when u k is applied as an input to (2), the resulting cost is optimal for the distribution induced on the random variable z. This concept is formalized in the following definition, inspired by [31].…”

Section: A Notion Of Stable Optimizermentioning

confidence: 99%

“…where σ 2 min ( Ĝ) denotes the smallest singular value of Ĝ. Proof: The proof idea is similar to [31,Theorem 4.3]. By recalling that z = (G − Ĝ)ū + w k , a direct application of Theorem 2.4 yields:…”

Section: A Notion Of Stable Optimizermentioning

confidence: 99%

“…A notable exception is [30], which however does not account for the presence of noise, and results are limited to regret analysis. In contrast, when the disturbance terms are unknown, the distributions of the random variables that characterize the cost are parametrized by the decision variables, thus leading to a stochastic optimization problem with decision-dependent distributions, as studied in [31]- [33]. In this work, we build upon this class of problems, but accounting for two additional complexities: the online nature of the optimization method and the coupling with a dynamical system.…”

Section: Introductionmentioning

confidence: 99%

“…One fundamental challenge in the design of the controller is that an error in the estimated transfer function leads to a stochastic optimization problem with decision-dependent distribution [33], that is, the optimization variable induces a shift in the distribution of the underlying random variables that parametrize the cost. This is a class of problems whose direct solution is intractable in general [31]. To bypass this hurdle, we leverage the notion of stable optimizer [31], [32], and we develop a stochastic controller that regulates the system towards such optimizer, up to an asymptotic error that depends on the time-variability of the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

“…This is a class of problems whose direct solution is intractable in general [31]. To bypass this hurdle, we leverage the notion of stable optimizer [31], [32], and we develop a stochastic controller that regulates the system towards such optimizer, up to an asymptotic error that depends on the time-variability of the optimization problem. We show that the controller exhibits strict contractivity with respect to the stable optimizers in expectation, and we explicitly quantify its transient performance.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis

Bianchin¹,

Vaquero²,

Cortés³

et al. 2021

Preprint

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This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available methods critically rely on a precise knowledge of the system dynamics (thus requiring off-line system identification and model refinement). To this aim, in this paper we first show that the steady-state transfer function of a linear system can be computed directly from control experiments, bypassing explicit model identification. Then, we leverage the estimated transfer function to design a controller -which is inspired by stochastic gradient descent methods -that regulates the system to the solution of the prescribed optimization problem. A distinguishing feature of our methods is that they do not require any knowledge of the system dynamics, disturbance terms, or their distributions. Our technical analysis combines concepts and tools from behavioral system theory, stochastic optimization with decision-dependent distributions, and stability analysis. We illustrate the applicability of the framework on a case study for mobility-on-demand ride service scheduling in Manhattan, NY.

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Section: A Notion Of Stable Optimizermentioning

confidence: 99%

Section: A Notion Of Stable Optimizermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis

Bianchin¹,

Vaquero²,

Cortés³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

Managing Performative Models

Khosrowi

2023

Philosophy of the Social Sciences

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Scientific models can be performative: they can causally affect the phenomena they are intended to represent. The existing literature offers two responses. The appraisal view emphasizes that performativity can sometimes be a good-making model attribute, e.g., when predictions steer the public’s behavior in desirable ways. The mitigation view seeks to endogenize agents’ behavioral response to model-issued forecasts to get rid of performativity instead. This paper argues that neither approach is fully compelling: the appraisal view encounters severe concerns about moral values illegitimately encroaching on how modelers construct and use models, while the mitigation view fails to acknowledge that endogenization is itself a choice that involves substantive value-judgments relating to the desirability of certain social outcomes.

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Classification with Few Tests through Self-Selection

Zhang

Conitzer

2021

AAAI

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We study test-based binary classification, where a principal either accepts or rejects agents based on the outcomes they get in a set of tests. The principal commits to a policy, which consists of all sets of outcomes that lead to acceptance. Each agent is modeled by a distribution over the space of possible outcomes. When an agent takes a test, he pays a cost and receives an independent sample from his distribution as the outcome. Agents can always choose between taking another test and stopping. They maximize their expected utility, which is the value of acceptance if the principal's policy accepts the set of outcomes they have and 0 otherwise, minus the total cost of tests taken. We focus on the case where agents can be either "good" or "bad" (corresponding to their distribution over test outcomes), and the principal's goal is to accept good agents and reject bad ones. We show, roughly speaking, that as long as the good and bad agents have different distributions (which can be arbitrarily close to each other), the principal can always achieve perfect accuracy, meaning good agents are accepted with probability 1, and bad ones are rejected with probability 1. Moreover, there is a policy achieving perfect accuracy under which the maximum number of tests any agent needs to take is constant — in sharp contrast to the case where the principal directly observes samples from agents' distributions. The key technique is to choose the policy so that agents self-select into taking tests.

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Performative Prediction

Cited by 7 publications

References 20 publications

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis

Managing Performative Models

Classification with Few Tests through Self-Selection

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