Distributed computing with adaptive heuristics
This presentation is the property of its rightful owner.
Sponsored Links
1 / 23

Distributed Computing with Adaptive Heuristics PowerPoint PPT Presentation


  • 45 Views
  • Uploaded on
  • Presentation posted in: General

Distributed Computing with Adaptive Heuristics. Aaron D. Jaggard Rutgers/Colgate. Michael Schapira Princeton Innovations in Computer Science 09 January 2011 Partially supported by NSF. Rebecca N. Wright Rutgers. This Talk.

Download Presentation

Distributed Computing with Adaptive Heuristics

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Distributed computing with adaptive heuristics

Distributed Computingwith Adaptive Heuristics

Aaron D. Jaggard

Rutgers/Colgate

Michael Schapira

Princeton

Innovations in Computer Science

09 January 2011

Partially supported by NSF

Rebecca N. Wright

Rutgers


This talk

This Talk

  • Identify new aspects of the boundary between game theory and distributed computing

  • Look at some initial results

  • Identify various avenues for future work


Background areas

Background Areas

Game Dynamics

(Natural Behaviors)

DistributedComputing

simple, myopic rules of behavior;

convergence in synchronized environment

nodes interacting in an asynchronous environment


Motivation

Motivation

Many real-world settings involve both simple, myopic behavior and asynchronicity

  • Network protocols

    • Routing

    • Congestion control

    • ...

  • Asynchronous circuits


Research agenda

Research Agenda

Distributed Computing with Adaptive Heuristics(BGP, TCP, … )

new questions

in game theory and economics

(fictitious play, regret minimization,…)

novel applications in distributed computing

(congestion control, asynchronous circuits,…)

Goal: Explore dynamics of adaptive heuristics when asynchrony is allowed


Understanding when dynamics converge a simple example

Understanding when Dynamics Converge: A Simple Example

  • Two stable states (pure Nash equilibria)

Bach

Stravinsky

(5,4)

(1,1)

Bach

(0,0)

(4,5)

Stravinsky


Understanding when dynamics converge a simple example1

Understanding when Dynamics Converge: A Simple Example

  • If either player is activated alone, the system converge

Bach

Stravinsky

(5,4)

(1,1)

Bach

(0,0)

(4,5)

Stravinsky


Understanding when dynamics converge a simple example2

Understanding when Dynamics Converge: A Simple Example

  • Without control over who is activated, the system might not converge

Bach

Stravinsky

(5,4)

(1,1)

Bach

(0,0)

(4,5)

Stravinsky


Basic model

Basic Model

  • n nodes (the players)

  • Node i has action space Ai

  • Each node i has a reaction function

    fi: A1 x A2 x ...xAn→Ai that determines i’s next

    action based on other current actions

    • No dependence on own action


Dynamics

Dynamics

  • Infinite sequence of discrete timestepst = 1, …

  • Schedule s:{1,…} → 2[n] determines which set of players is activated at time t.

    • Fair schedules

  • Start at an initial state; at each time step t, let the nodes in s(t) react using their reaction functions


Convergence

Convergence

  • The players’ action profile a=(a1,…, an) is a stable state if fi(a) = ai for every i.

  • The system is convergent if the dynamics always converge (for all initial states and all fair schedules)


Two high level questions

Two High-Level Questions

  • What classes of systems are guaranteed (or cannot be guaranteed) to always converge to a stable state?

  • How hard is it to determine whether a system always converges to a stable state?


Basic result

Basic Result

Theorem: If the system has multiple stable states, then the system is not convergent. (I.e., there is some initial state and some schedule that diverge.)

  • Actually, can strengthen this:

    • Allow some history-dependence

    • Allow randomness in reaction functions


Revisiting our example

Revisiting Our Example

Bach

Stravinsky

(5,4)

(1,1)

Bach

(0,0)

(4,5)

Stravinsky


A few words about the proof

A Few Words About the Proof

  • Inspired by approach to FLP result on impossibility of resilient consensus


Applications

Applications

  • Interdomain routing

  • Congestion control

  • Best-reply dynamics in general games

  • Diffusion of technologies in social networks

  • Asynchronous circuits


Communication complexity

Communication Complexity

Theorem: Determining whether a system of n nodes, each with two actions, is convergent may require Ω(2n) bits.

  • Even if all reaction functions are deterministic, and do not depend on history or own action

  • Uses a reduction from SET DISJOINTNESS.

    • Constructed system has a unique stable state


  • Computational complexity

    Computational Complexity

    Theorem: Determining whether a system of n nodes, each with deterministic and historyless reaction function, is convergent is PSPACE-complete.

    • So, difficult even if the reaction functions are succinctly represented (so that they could be transmitted quickly)

    • Under complexity assumptions, no short witnesses (in general) of being convergent


    Scheduling

    Scheduling

    Question: Does randomness help?

    Bach

    Stravinsky

    (5,4)

    (1,1)

    Bach

    (0,0)

    (4,5)

    Stravinsky


    Scheduling1

    Scheduling

    Question: Does randomness help?

    Answer: No. Divergence may not only be possible, but overwhelmingly likely.

    • Issues of r-fairness


    Open questions

    Open Questions

    • What are the convergence guarantees and impossibility results

      • For other heuristics

      • For other notions of convergence

      • For other notions of equilibrium

    • We’ve taken first steps in the context of regret-minimizing dynamics


    Other open questions

    Other Open Questions

    • Variations in information

      • Outdated information

      • Knowledge only of own utility function (uncoupled dynamics)

    • Lots of others


    Summary

    Summary

    • Simple behaviors show up in lots of settings

      • Important to understand dynamic behavior when asynchrony is allowed

    • Initial results on the impossibility of guaranteeing convergence

    • Lots of open questions

      • What can we say about the dynamic behavior in other natural asynchronous settings?


  • Login