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Author (up) Bravo, M.; Cominetti, R.
Title Sharp convergence rates for averaged nonexpansive maps Type
Year 2018 Publication Israel Journal Of Mathematics Abbreviated Journal Isr. J. Math.
Volume 227 Issue 1 Pages 163-188
Keywords
Abstract We establish sharp estimates for the convergence rate of the Kranosel'skiA-Mann fixed point iteration in general normed spaces, and we use them to show that the optimal constant of asymptotic regularity is exactly . To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. We show that these bounds are tight by building a nonexpansive map T: [0, 1](N) -> [0, 1](N) that attains them with equality, settling a conjecture by Baillon and Bruck. The recursive bounds are in turn reinterpreted as absorption probabilities for an underlying Markov chain which is used to establish the tightness of the constant 1/root pi.
Address [Bravo, Mario] Univ Santiago Chile, Dept Matemat & Ciencia Computac, Alameda Libertador Bernardo Ohiggins 3363, Santiago, Chile, Email: mario.bravo.g@usach.cl;
Corporate Author Thesis
Publisher Hebrew Univ Magnes Press Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0021-2172 ISBN Medium
Area Expedition Conference
Notes WOS:000442512900006 Approved
Call Number UAI @ eduardo.moreno @ Serial 909
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Author (up) Bravo, M.; Cominetti, R.; Pavez-Signe, M.
Title Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces Type
Year 2019 Publication Mathematical Programming Abbreviated Journal Math. Program.
Volume 175 Issue 1-2 Pages 241-262
Keywords Nonexpansive maps; Fixed point iterations; Rates of convergence; Evolution equations
Abstract We study the convergence of an inexact version of the classical Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps. Our main result establishes a new metric bound for the fixed-point residuals, from which we derive their rate of convergence as well as the convergence of the iterates towards a fixed point. The results are applied to three variants of the basic iteration: infeasible iterations with approximate projections, the Ishikawa iteration, and diagonal Krasnosels'kii-Mann schemes. The results are also extended to continuous time in order to study the asymptotics of nonautonomous evolution equations governed by nonexpansive operators.
Address [Bravo, Mario] Univ Santiago Chile, Dept Matemat & Ciencia Comp, Alameda Libertador Bernardo Ohiggins 3363, Santiago, Chile, Email: mario.bravo.g@usach.cl;
Corporate Author Thesis
Publisher Springer Heidelberg Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0025-5610 ISBN Medium
Area Expedition Conference
Notes WOS:000465626900008 Approved
Call Number UAI @ eduardo.moreno @ Serial 997
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Author (up) Colini-Baldeschi, R.; Cominetti, R.; Mertikopoulos, P.; Scarsini, M.
Title When Is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic Type
Year 2020 Publication Operations Research Abbreviated Journal Oper. Res.
Volume 68 Issue 2 Pages 411-434
Keywords nonatomic congestion games; price of anarchy; light traffic; heavy traffic; regular variation
Abstract This paper examines the behavior of the price of anarchy as a function of the traffic inflow in nonatomic congestion games with multiple origin/destination (O/D) pairs. Empirical studies in real-world networks show that the price of anarchy is close to 1 in both light and heavy traffic, thus raising the following question: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain a positive distance away from 1 for all values of the traffic inflow, even in simple three-link networks with a single O/D pair and smooth, convex costs. On the other hand, for a large class of cost functions (including all polynomials) and inflow patterns, the price of anarchy does converge to 1 in both heavy and light traffic, irrespective of the network topology and the number of O/D pairs in the network. We also examine the rate of convergence of the price of anarchy, and we show that it follows a power law whose degree can be computed explicitly when the network's cost functions are polynomials.
Address [Colini-Baldeschi, Riccardo] Facebook Inc, Core Data Sci Grp, London W1T 1FB, England, Email: rickuz@fb.com;
Corporate Author Thesis
Publisher Informs Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0030-364x ISBN Medium
Area Expedition Conference
Notes WOS:000521730200006 Approved
Call Number UAI @ eduardo.moreno @ Serial 1128
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Author (up) Colini-Baldeschi, R.; Cominetti, R.; Scarsini, M.
Title Price of Anarchy for Highly Congested Routing Games in Parallel Networks Type
Year 2019 Publication Theory Of Computing Systems Abbreviated Journal Theor. Comput. Syst.
Volume 63 Issue 1 Pages 90-113
Keywords Nonatomic routing games; Price of Anarchy; Regularly varying functions; Wardrop equilibrium; Parallel networks; High congestion
Abstract We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.
Address [Colini-Baldeschi, Riccardo; Scarsini, Marco] LUISS, Dipartimento Econ & Finanza, Viale Romania 32, I-00197 Rome, Italy, Email: rcolini@luiss.it;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1432-4350 ISBN Medium
Area Expedition Conference
Notes WOS:000456320200005 Approved
Call Number UAI @ eduardo.moreno @ Serial 974
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Author (up) Cominetti, R.; Correa, J.; Olver, N.
Title Long-Term Behavior of Dynamic Equilibria in Fluid Networks Type
Year 2022 Publication Operations Research Abbreviated Journal Oper. Res.
Volume 70 Issue 1 Pages 516-526
Keywords flows over time; dynamic equilibria; steady state
Abstract A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair, and each link has a per-time-unit capacity and a transit time. A dynamic equilibrium (or equilibrium flow over time) is a flow pattern over time such that no flow particle has incentives to unilaterally change its path. Although the model has been around for almost 50 years, only recently results regarding existence and characterization of equilibria have been obtained. In par-ticular, the long-term behavior remains poorly understood. Our main result in this paper is to show that, under a natural (and obviously necessary) condition on the queuing capacity, a dynamic equilibrium reaches a steady state (after which queue lengths remain constant) in finite time. Previously, it was not even known that queue lengths would remain bounded. The proof is based on the analysis of a rather nonobvious potential function that turns out to be monotone along the evolution of the equilibrium. Furthermore, we show that the steady state is characterized as an optimal solution of a certain linear program. When this program has a unique solution, which occurs generically, the long-term behavior is completely predictable. On the contrary, if the linear program has multiple solutions, the steady state is more difficult to identify as it depends on the whole temporal evolution of the equilibrium.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0030-364X ISBN Medium
Area Expedition Conference
Notes WOS:000708986100001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1472
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Author (up) Cominetti, R.; Dose, V.; Scarsini, M.
Title The price of anarchy in routing games as a function of the demand Type
Year 2022 Publication Mathematical Programming Abbreviated Journal Math. Program.
Volume Early Access Issue Pages
Keywords Nonatomic routing games; Price of anarchy; Affine cost functions; Variable demand
Abstract The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0025-5610 ISBN Medium
Area Expedition Conference
Notes WOS:000693858200001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1468
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Author (up) Cominetti, R.; Quattropani, M.; Scarsini, M.
Title The Buck-Passing Game Type
Year 2022 Publication Mathematics Operations Research Abbreviated Journal Math. Oper. Res.
Volume Early Access Issue Pages
Keywords prior-free equilibrium; generalized ordinal potential game; finite improvement property; fairness of equilibria; price of anarchy; price of stability; Markov chain tree theorem; PageRank; PageRank game
Abstract We consider two classes of games in which players are the vertices of a directed graph. Initially, nature chooses one player according to some fixed distribution and gives the player a buck. This player passes the buck to one of the player's out-neighbors in the graph. The procedure is repeated indefinitely. In one class of games, each player wants to minimize the asymptotic expected frequency of times that the player receives the buck. In the other class of games, the player wants to maximize it. The PageRank game is a particular case of these maximizing games. We consider deterministic and stochastic versions of the game, depending on how players select the neighbor to which to pass the buck. In both cases, we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. If the graph on which the game is played admits a Hamiltonian cycle, then this is the outcome of prior-five Nash equilibrium in the minimizing game. For the minimizing game, we then use the price of anarchy and stability to measure fairness of these equilibria.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0364-765X ISBN Medium
Area Expedition Conference
Notes WOS:000731930100001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1502
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Author (up) Cominetti, R.; Roshchina, V.; Williamson, A.
Title A counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections Type
Year 2019 Publication Optimization Abbreviated Journal Optimization
Volume 68 Issue 1 Pages 3-12
Keywords Cyclic projections; under-relaxed projections; De Pierro conjecture
Abstract The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the -under-relaxed cyclic projection method converge when towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in for which the -under-relaxed cycles do not converge.
Address [Cominetti, Roberto] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: v.roshchina@unsw.edu.au
Corporate Author Thesis
Publisher Taylor & Francis Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0233-1934 ISBN Medium
Area Expedition Conference
Notes WOS:000459733300002 Approved
Call Number UAI @ eduardo.moreno @ Serial 987
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Author (up) Contreras, J.P.; Cominetti, R.
Title Optimal error bounds for non-expansive fixed-point iterations in normed spaces Type
Year 2022 Publication Mathematical Programming Abbreviated Journal Math. Program.
Volume Early Access Issue Pages
Keywords Non-expansive maps; Fixed-point iterations; Error bounds; Convergence rates
Abstract This paper investigates optimal error bounds and convergence rates for general Mann iterations for computing fixed-points of non-expansive maps. We look for iterations that achieve the smallest fixed-point residual after n steps, by minimizing a worst-case bound parallel to x(n) – Tx(n)parallel to <= R-n derived from a nested family of optimal transport problems. We prove that this bound is tight so that minimizing R-n yields optimal iterations. Inspired from numerical results we identify iterations that attain the rate R-n = O(1/n), which we also show to be the best possible. In particular, we prove that the classical Halpern iteration achieves this optimal rate for several alternative stepsizes, and we determine analytically the optimal stepsizes that attain the smallest worst-case residuals at every step n, with a tight bound R-n approximate to 4/n+4. We also determine the optimal Halpern stepsizes for affine non-expansive maps, for which we get exactly R-n = 1/n+1. Finally, we show that the best rate for the classical Krasnosel'skii-Mann iteration is Si (11 Omega(1/root n), and present numerical evidence suggesting that even extended variants cannot reach a faster rate.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN ISBN Medium
Area Expedition Conference
Notes WOS:000805887100002 Approved
Call Number UAI @ alexi.delcanto @ Serial 1577
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Author (up) Dumett, M.A.; Cominetti, R.
Title On The Stability Of An Adaptive Learning Dynamics In Traffic Games Type
Year 2018 Publication Journal Of Dynamics And Games Abbreviated Journal J. Dyn. Games
Volume 5 Issue 4 Pages 265-282
Keywords Congestion games; adaptive learning dynamics; stochastic algorithms; routing equilibrium; dynamical systems; stability; Routh-Hurwitz criterion
Abstract This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.
Address [Dumett, Miguel A.] San Diego State Univ, Computat Sci Res Ctr, San Diego, CA 92182 USA, Email: mdumett@sdsu.edu;
Corporate Author Thesis
Publisher Amer Inst Mathematical Sciences-Aims Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2164-6066 ISBN Medium
Area Expedition Conference
Notes WOS:000450339800001 Approved
Call Number UAI @ eduardo.moreno @ Serial 1035
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Author (up) Rios, I.; Larroucau, T.; Parra, G.; Cominetti, R.
Title Improving the Chilean College Admissions System Type
Year 2021 Publication Operations Research Abbreviated Journal Oper. Res.
Volume 69 Issue 4 Pages 1186-1205
Keywords college admissions; stable assignment; flexible quotas; nonstrict preferences
Abstract In this paper we present the design and implementation of a new system to solve the Chilean college admissions problem. We develop an algorithm that obtains all applicant/program pairs that can be part of a stable allocation when preferences are not strict and when all students tied in the last seat of a program (if any) must be allocated. We use this algorithm to identify which mechanism was used in the past to perform the allocation, and we propose a new method to incorporate the affirmative action that is part of the system to correct the inefficiencies that arise from having double-assigned students. By unifying the regular admission with the affirmative action, we have improved the allocation of approximately 2.5% of students assigned every year since 2016. From a theoretical standpoint, we show that some desired properties, such as strategy-proofness and monotonicity, cannot be guaranteed under flexible quotas.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0030-364X ISBN Medium
Area Expedition Conference
Notes WOS:000684548900010 Approved
Call Number UAI @ alexi.delcanto @ Serial 1455
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