Personalized optimization with user’s feedback

Simonetto, Andrea; Dall’Anese, Emiliano; Monteil, Julien; Bernstein, Andrey

doi:10.1016/j.automatica.2021.109767

Cited by 22 publications

(25 citation statements)

References 52 publications

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“…This assumption is not so stringent as it may seem. In the example considered above, i.e., agents endowed with learning procedures, asymptotic consistency bounds on the approximation error can be exploited directly [28].…”

Section: B Inexact Br Computation In Exact Potential Gamesmentioning

confidence: 99%

Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems

Fabiani¹,

Franci²,

Sagratella³

et al. 2022

Preprint

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We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the agents update through iterations by choosing an exact optimal strategy; ii) the game admits an exact potential and the agents adopt approximated optimal responses. By exploiting the properties of integer-compatible regularization functions used as penalty terms affecting the local cost function of each agent, we are able to show that both algorithms converge to either an exact or an ǫ-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.

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Section: B Inexact Br Computation In Exact Potential Gamesmentioning

confidence: 99%

Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems

Fabiani¹,

Franci²,

Sagratella³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The goal is to drive the population to an GNE. The reconstructed information is thereby exploited by the coordinator to design parametric personalized incentives for the agents [11], [37], [38]. On its side, the population of agents receives those personalized incentives, computes a solution, i.e., a variational generalized Nash equilibrium (v-GNE), to an extended game by means of available algorithms in the inner loop, and then returns feedback measures to the coordinator.…”

Section: B Main Contributionsmentioning

confidence: 99%

“…Thus, we assume to do not have an expression for θ(x; t) that can be exploited directly for the equilibrium seeking algorithm design. To address these crucial issues, we design personalized feedback functionals u i : R n × N → R in the spirit of [11], [37]- [39], which are used as "control actions" in the two-layer semi-decentralized scheme depicted in Fig. 1.…”

Section: B Main Challenges and Technical Considerationsmentioning

confidence: 99%

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Personalized incentives as feedback design in generalized Nash equilibrium problems

Fabiani¹,

Simonetto²,

Goulart³

2022

Preprint

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We investigate both stationary and time-varying, nonmonotone generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision a scenario in which the formal expression of the underlying potential function is not available, and we design a semi-decentralized Nash equilibrium seeking algorithm.In the proposed two-layer scheme, a coordinator iteratively integrates the (possibly noisy and sporadic) agents' feedback to learn the pseudo-gradients of the agents, and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measurements to the coordinator. In the stationary setting, our algorithm returns a Nash equilibrium in case the coordinator is endowed with standard learning policies, while it returns a Nash equilibrium up to a constant, yet adjustable, error in the time-varying case. As a motivating application, we consider the ridehailing service provided by several companies with mobility as a service orchestration, necessary to both handle competition among firms and avoid traffic congestion, which is also adopted to run numerical experiments verifying our results.

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“…The engineering cost can be related to operational efficiency and may capture objectives such as aggregate setpoint tracking when devices aggregate in a virtual power-plant fashion; it is time-varying [8] in a sense that it captures time-varying objectives (e.g., tracking of a power setpoint that evolves over time), dynamic pricing, or real time measurements. In lieu of synthetic mathematical models for the user's functions (based on e.g., statistics or averaged models), this paper leverages Gaussian Processes (GPs) [9], [10] to learn the function from data (e.g., users' feedback). Approximating a function A. Ospina and E. Dall'Anese are with the Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO, USA; e-mails: ana.ospina, emiliano.dallanese@colorado.edu.…”

Section: Introductionmentioning

confidence: 99%

Personalized Demand Response via Shape-Constrained Online Learning

Ospina¹,

Simonetto²,

Dall’Anese³

2020

Preprint

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This paper formalizes a demand response task as an optimization problem featuring a known time-varying engineering cost and an unknown (dis)comfort function. Based on this model, this paper develops a feedback-based projected gradient method to solve the demand response problem in an online fashion, where: i) feedback from the user is leveraged to learn the (dis)comfort function concurrently with the execution of the algorithm; and, ii) measurements of electrical quantities are used to estimate the gradient of the known engineering cost. To learn the unknown function, a shape-constrained Gaussian Process is leveraged; this approach allows one to obtain an estimated function that is strongly convex and smooth. The performance of the online algorithm is analyzed by using metrics such as the tracking error and the dynamic regret. A numerical example is illustrated to corroborate the technical findings. √x x. A vector of zeros is represented by 0 and a vector of ones by 1, with the corresponding dimensions. O refers to the big O notation; that is, given two positive sequences {a k } ∞ k=0 and {b k } ∞ k=0 , we say that

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Personalized optimization with user’s feedback

Cited by 22 publications

References 52 publications

Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems

Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems

Personalized incentives as feedback design in generalized Nash equilibrium problems

Personalized Demand Response via Shape-Constrained Online Learning

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