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Nov 28, '22November 28, 2022
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Nov 29, '22November 29, 2022
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Dec 1, '22December 1, 2022●(1 event)
Séminaire Stephane DurandSéminaire Stephane Durand – Jeux de contagions et d'influences: les différentes formes, les approches et le contexte |
Dec 2, '22December 2, 2022
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Dec 3, '22December 3, 2022
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Dec 4, '22December 4, 2022
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31October 31, 2022
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November1November 1, 2022 |
2November 2, 2022
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3November 3, 2022
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4November 4, 2022
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5November 5, 2022
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6November 6, 2022
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7November 7, 2022
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8November 8, 2022
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9November 9, 2022
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Verimag seminar: Stephan Plassart – Total Flow Analysis (TFA) is a method for conducting the worst-case analysis of time sensitive networks without cyclic dependencies. In networks with cyclic dependencies, Fixed-Point TFA introduces artificial cuts, analyses the resulting cycle-free network with TFA, and iterates. If it converges, it does provide valid performance bounds. We show that the choice of the specific cuts used by Fixed-Point TFA does not affect its convergence nor the obtained performance bounds, and that it can be replaced by an alternative algorithm that does not use any cut at all, while still applying to cyclic dependencies. Room: 206 Bâtiment IMAG (206) |
11November 11, 2022
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12November 12, 2022
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13November 13, 2022
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14November 14, 2022
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15November 15, 2022
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16November 16, 2022
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Seminar Olivier Bilenne – Solutions of Poisson's equation for first-policy improvement in parallel queueing systems
This talk addresses the problem of (state-aware) job dispatching at minimum long-run average cost in a parallel queueing system with Poisson arrivals. Policy iteration is a technique for approaching optimality through improvement of an initial dispatching policy. Its implementation rests on the computation of value functions. In this context, we will consider the M/G/1-FCFS queue endowed with an arbitrary cost function for the waiting times of the incoming jobs. The associated relative value function is a solution of Poisson's equation for Markov chains, which I propose to solve in the Laplace transform domain by considering an ancillary stochastic process extended to (imaginary) negative backlog states. This construction enables us to issue closed-form solutions for simple cost functions (polynomial, exponential, and their piecewise compositions), in turn permitting the derivation of interval bounds for the relative value functions to more general cost functions. Such bounds allow for an exact implementation of the first improvement step of policy iteration in a parallel queueing system.
One objective of the talk is to identify the main obstacles to the implementation of the policy iteration algorithm in parallel queueing systems; the purpose then to discuss the new directions that transform domain analysis might offer beyond first policy improvement.
Further reading: Olivier Bilenne. Dispatching to parallel servers: solutions of Poisson's equation for first-policy improvement. Queueing Systems, Springer Verlag, 2021, Queueing Systems, 99 (3), pp.199-230. https://hal.archives-ouvertes.fr/hal-02925284
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18November 18, 2022
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19November 19, 2022
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20November 20, 2022
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21November 21, 2022
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22November 22, 2022
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23November 23, 2022
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24November 24, 2022
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25November 25, 2022
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26November 26, 2022
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27November 27, 2022
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28November 28, 2022
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29November 29, 2022
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30November 30, 2022
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December1December 1, 2022●(1 event)Séminaire Stephane Durand – Jeux de contagions et d'influences: les différentes formes, les approches et le contexte |
2December 2, 2022
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3December 3, 2022
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4December 4, 2022
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5December 5, 2022
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6December 6, 2022
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7December 7, 2022
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Séminaire GLSI / CtrlA: Quentin Guilloteau (Datamove) – Bâtiment IMAG (442) Seminar Mario Bravo (room 106) – |
9December 9, 2022
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10December 10, 2022
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11December 11, 2022
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Seminar Matthieu Jonckheere (room 306) – Title: Parameter Selection in Fermat Distances: Navigating Geometry and Noise |
13December 13, 2022
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14December 14, 2022
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PhD defense Chen Yan: Poliques quasi-optimal pour les restless bandits. – Thèse supervisée par Nicolas GAST et Bruno GAUJAL.
La soutenance aura lieu le jeudi 15 décembre 2022 à 14h00 à l'amphithéâtre 1 de la Tour IRMA (51 rue des mathématiques, 38610 Gières). Un pot aura lieu après la soutenance à salle 406 du bâtiment IMAG.
Jury:
-- David Alan Goldberg, Professeur associé, Université de Cornell (Rapporteur)
-- Bruno Scherrer, Chargé de recherche, Inria Nancy (Rapporteur)
-- Jérôme Malick, Directeur de recherche, CNRS (Examinateur)
-- Nguyễn Kim Thắng, Professeur, Université Grenoble Alpes (Examinateur)
-- LEGROS Benjamin, Professeur associé, EM Normandie (Examinateur)
Résumé :
Bandits are one of the most basic examples of decision-making with uncertainty. A Markovian restless bandit can be seen as the following sequential allocation problem: At each decision epoch, one or several arms are activated (pulled); all arms generate an instantaneous reward that depend on their state and their activation; the state of each arm then changes in a Markovian fashion, based on an underlying transition matrix. Both the rewards and the probability matrices are known, and the new state is revealed to the decision maker for its next decision. The word restless serves to emphasize the fact that arms that are not activated can also change states, hence generalizes the simpler rested bandits. In principle, the above problem can be solved by dynamic programming, since it is a Markov decision process. The challenge that we face is the curse of dimension, since the size of possible states and actions grows exponentially with the number of arms of the bandit. Consequently, the focus is to design policies that solve the dilemma of computational efficiency and close-to-optimal performance.
In this thesis, we construct computationally efficient policies with provable performance bounds, that may differ depending on certain properties of the problem. We first investigate the classical Whittle index policy (WIP) on infinite horizon problems, and prove that if it is asymptotically optimal under the global attractor assumption, then almost always it converges to the optimal value exponentially fast. The application of WIP has the additional technical assumption of indexability as a prerequisite, to get around this, we next study the LP-index policy, that is well-defined for any problem, and shares the same exponential speed of convergence as WIP under similar assumptions.
In infinite horizon, we always need the global attractor assumption for asymptotic optimality. We next study the problem under finite horizon, so that this assumption is no-longer a concern. Instead, the LP-compatibility and the non-degeneracy are required for the asymptotic optimality and a faster convergence rate. We construct the finite horizon LP-index policy, as well as the LP-update policy, that amounts to solving new LP-index policies during the evolution of the process. This latter LP-update policy is then generalized to the broader framework of weakly coupled MDPs, together with the generalization of the non-degenerate condition. This condition also allows a more efficient implementation of the LP-update policy, as well as a faster convergence rate, if it is satisfied on the weakly coupled MDPs.
Tour IRMA, campus Saint Martin d'Hères |
16December 16, 2022
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17December 17, 2022
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18December 18, 2022
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19December 19, 2022
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20December 20, 2022
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21December 21, 2022
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22December 22, 2022
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23December 23, 2022
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24December 24, 2022
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25December 25, 2022
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26December 26, 2022
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27December 27, 2022
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28December 28, 2022
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29December 29, 2022
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30December 30, 2022
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31December 31, 2022
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January1January 1, 2023 |
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