Data-Driven Regret Minimization in Routing Games under Uncertainty

Dietrich, Jonathan; Hota, Ashish R.; Cherukuri, Ashish

doi:10.23919/ecc.2019.8795664

Cited by 2 publications

(1 citation statement)

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“…Therefore, to estimate equilibrium flow, some works solve a stochastic nonlinear complementarity problem [7], either in an expectation basis [8], [9] or in a robust manner [10], [11]. In [12], equilibrium flow is hypothesized to be the minimizer of the regret experienced by users. These approaches might be too conservative or might not account for the risk-sensitive behavior of agents.…”

Section: Introductionmentioning

confidence: 99%

Sample average approximation of CVaR-based Wardrop equilibrium in routing under uncertain costs

Cherukuri

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper focuses on the class of routing games that have uncertain costs. Assuming that agents are riskaverse and select paths with minimum conditional value-atrisk (CVaR) associated to them, we define the notion of CVaRbased Wardrop equilibrium (CWE). We focus on computing this equilibrium under the condition that the distribution of the uncertainty is unknown and a set of independent and identically distributed samples is available. To this end, we define the sample average approximation scheme where CWE is estimated with solutions of a variational inequality problem involving sample average approximations of the CVaR. We establish two properties for this scheme. First, under continuity of costs and boundedness of uncertainty, we prove asymptotic consistency, establishing almost sure convergence of approximate equilibria to CWE as the sample size grows. Second, under the additional assumption of Lipschitz cost, we prove exponential convergence where the probability of the distance between an approximate solution and the CWE being smaller than any constant approaches unity exponentially fast. Simulation example validates our theoretical findings.

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Section: Introductionmentioning

confidence: 99%

Sample average approximation of CVaR-based Wardrop equilibrium in routing under uncertain costs

Cherukuri

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Routing Games in the Wild: Efficiency, Equilibration, Regret, and a Price of Anarchy Bound via Long Division

Monnot¹,

Benita

Piliouras

2022

ACM Trans. Econ. Comput.

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Routing games are amongst the most well studied domains of game theory. How relevant are these pen-and-paper calculations to understanding the reality of everyday traffic routing? We focus on a semantically rich dataset that captures detailed information about the daily behavior of thousands of Singaporean commuters and examine the following basic questions: - Does the traffic stabilize? - Is the system behavior consistent with latency-minimizing agents? - Is the resulting system efficient? In order to capture the efficiency of the traffic network in a way that agrees with our everyday intuition we introduce a new metric, the Free-flow Index (FFI) , which reflects the inefficiency resulting from system congestion. Along the way, we provide the first model-free computation of an upper bound to the price of anarchy utilizing only real world measurements of traffic data.

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Data-Driven Regret Minimization in Routing Games under Uncertainty

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Cited by 2 publications

References 20 publications

Sample average approximation of CVaR-based Wardrop equilibrium in routing under uncertain costs

Sample average approximation of CVaR-based Wardrop equilibrium in routing under uncertain costs

Routing Games in the Wild: Efficiency, Equilibration, Regret, and a Price of Anarchy Bound via Long Division

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