Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Models

Barazandeh, Babak; Ghafelebashi, Ali; Razaviyayn, Meisam; Sriharsha, Ram

doi:10.48550/arxiv.2105.05953

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…This formulation is amenable to the ADMM method [67][68][69][70][71][72], which has a natural distributed implementation. Our ADMM formulation (8) shows that this computation burden can be distributed among drivers' cell phones.…”

Section: Algorithm For Offering Incentives and A Distributed Implemen...mentioning

confidence: 99%

Congestion Reduction via Personalized Incentives

Ghafelebashi¹,

Razaviyayn²,

Dessouky³

2022

Preprint

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With rapid population growth and urban development, traffic congestion has become an inescapable issue, especially in large cities. Many congestion reduction strategies have been proposed in the past, ranging from roadway extension to transportation demand management. In particular, congestion pricing schemes have been used as negative reinforcements for traffic control. In this project, we study an alternative approach of offering positive incentives to drivers to take different routes. More specifically, we propose an algorithm to reduce traffic congestion and improve routing efficiency via offering personalized incentives to drivers. We exploit the wide-accessibility of smart devices to communicate with drivers and develop an incentive offering mechanism using individuals' preferences and aggregate traffic information. The incentives are offered after solving a large-scale optimization problem in order to minimize the total travel time (or minimize any cost function of the network such as total Carbon emission). Since this massive size optimization problem needs to be solved continually in the network, we developed a distributed computational approach. The proposed distributed algorithm is guaranteed to converge under a mild set of assumptions that are verified with real data. We evaluated the performance of our algorithm using traffic data from the Los Angeles area. Our experiments show congestion reduction of up to 11% in arterial roads and highways.

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Section: Algorithm For Offering Incentives and A Distributed Implemen...mentioning

confidence: 99%

Congestion Reduction via Personalized Incentives

Ghafelebashi¹,

Razaviyayn²,

Dessouky³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A solution to this problem corresponds to finding a Nash equilibrium point [23], for which several algorithms including Mirror-Prox [24] have been proposed, provided that the nature of the objective function is convex-concave. In general, solving min-max optimization problem is difficult which keeps other approaches attractive [25,26,27,28]. This is due to the fact that finding a Nash equilibrium point is computationally NP-hard in general [29]; therefore, the focus has shifted to finding a first-order Nash point (see upcoming section for more details) and numerous algorithms have been proposed to find such a point in non-convex-concave games [30], and non-convexnon-concave games under Polyak-Lojasiewicz (PL) [31] and Minty Variational Inequality (VI) [32] conditions.…”

Section: Introductionmentioning

confidence: 99%

A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems

Barazandeh,

Huang,

Michailidis

2021

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Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent efforts for solving them are limited to special regimes such as convex-concave games. Further, it is customarily assumed that the underlying optimization problem is solved either by a single machine or in the case of multiple machines connected in centralized fashion, wherein each one communicates with a central node. The latter approach becomes challenging, when the underlying communications network has low bandwidth. In addition, privacy considerations may dictate that certain nodes can communicate with a subset of other nodes. Hence, it is of interest to develop methods that solve min-max games in a decentralized manner. To that end, we develop a decentralized adaptive momentum (ADAM)-type algorithm for solving min-max optimization problem under the condition that the objective function satisfies a Minty Variational Inequality condition, which is a generalization to convex-concave case. The proposed method overcomes shortcomings of recent non-adaptive gradient-based decentralized algorithms for min-max optimization problems that do not perform well in practice and require careful tuning. In this paper, we obtain non-asymptotic rates of convergence of the proposed algorithm (coined Dadam 3 ) for finding a (stochastic) first-order Nash

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Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Models

Cited by 2 publications

References 26 publications

Congestion Reduction via Personalized Incentives

Congestion Reduction via Personalized Incentives

A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems

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