Machine Learning Applications in Grid Computing

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Machine Learning Applications in Grid Computing

• George Cybenko, Guofei Jiang and Daniel Bilar
• Thayer School of Engineering
• Dartmouth College
• 22th Sept.,1999, 37th Allerton Conference
• Urbana-Champaign, Illinois
• Acknowledgements
• This work was partially supported by AFOSR
  grants F49620-97-1-0382, NSF grant CCR-9813744
  and DARPA contract F30602-98-2-0107.

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Grid vision

• Grid computing refers to computing in a
  distributed networked environment in which
  computing and data resources are located
  throughout the network.
• Grid infrastructures provide basic infrastructure
  for computations that integrate geographically
  disparate resources, create a universal source of
  computing power that supports dramatically new
  classes of applications.
• Several efforts are underway to build
  computational grids such as Globus, Infospheres
  and DARPA CoABS.

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Grid services

• A fundamental capability required in grids is a
  directory service or broker that dynamically
  matches user requirements with available
  resources.
• Prototype of grid services

Request
Client
Server
Service
Service Location Request
Advertise
Reply
Matchmaker
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Matching conflicts

• Brokers and matchmakers use keywords and domain
  ontologies to specify services.
• Keywords and ontologies cannot be defined and
  interpreted precisely enough to make brokering or
  matchmaking between grid services robust in a
  truly distributed, heterogeneous computing
  environment.
• Matching conflicts exist between clients
  requested functionality and service providers
  actual functionality.

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An example

• A client requires a three-dimensional FFT. A
  request is made to a broker or matchmaker for a
  FFT service based on the keywords and possibly
  parameter lists.
• The broker or matchmaker uses the keywords to
  retrieve its catalog of services and returns with
  the candidate remote services.
• Literally dozens of different algorithms for FFT
  computations with different assumptions,
  dimensions, accuracy, input-output format and so
  on.
• The client must validate the actual functionality
  of these remote services before the client
  commits to use it.

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Functional validation

• Functional validation means that a client
  presents to a prospective service provider a
  sequence of challenges. The service provider
  replies to these challenges with corresponding
  answers. Only after the client is satisfied that
  the service providers answers are consistent
  with the clients expectations is an actual
  commitment made to using the service.
• Three steps
• Service identification and location.
• Service functional validation.
• Commitment to the service

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Our approach

• Challenge the service provider with some test
  cases x1, x2, ..., xk . The remote service
  provider R offers the corresponding answers
  fR(x1), fR(x2), ..., fR(xk). The client C may or
  may not have independent access to the answers
  fC(x1), fC(x2), ..., fC(xk).
• Possible situations and machine learning models
• C knows fC(x) and R provides fR(x).
• PAC learning and Chernoff bounds theory
• C knows fC(x) and R does not provide fR(x).
• Zero-knowledge proof
• C does not know fC(x) and R provides fR(x).
• Simulation-based learning and reinforcement
  learning

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Mathematical framework

• The goal of PAC learning is to use few examples
  as possible, and as little computation as
  possible to pick a hypothesis concept which is a
  close approximation to the target concept.
• Define a concept to be a boolean mapping
  . X is the input space. c(x)1
  indicates x is a positive example , i.e. the
  service provider can offer the correct service
  for challenge x.
• Define an index function
• Now define the error between the target concept
  c and the hypothesis h as
  .

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Mathematical framework(contd)

• The client can randomly pick m samples to PAC
  learn a hypothesis h about whether the service
  provider can offer the correct service .
• Theorem 1(Blumer et.al.) Let H be any
  hypothesis space of finite VC dimension d
  contained in , P be any probability
  distribution on X and the target concept c be
  any Borel set contained in X. Then for any
  , given the following m independent
  random examples of c drawn according to P , with
  probability at least , every
  hypothesis in H that is consistent with all of
  these examples has error at most .

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Simplified results

• Assuming that with regard to some concepts, all
  test cases have the same probability about
  whether the service provider can offer the
  correct service.
• Theorem 2(Chernoff bounds) Consider independent
  identically distributed samples ,
  from a Bernoulli distribution with expectation
  . Define the empirical estimate of based on
  these samples as
  
  
  Then for any , if
  the sample size , then the
  probability .
• Corollary 2.1 For the functional validation
  problem described above, given any
  , if the sample size , then the
  probability .

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Simplified results(contd)

• Given a target probability P, the client needs to
  know how many positive consecutive samples are
  required so that the next request to the service
  will be correct with probability P.
• So probabilities , and P have the
  following inequality
• Formulate the sample size problem as the
  following nonlinear optimization problem
  s.t.
  and

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Simplified results(contd)

• From the constraint inequality,
• Then transfer the above two dimensional function
  optimization problem to the one dimensional
  one s.t.
• Elementary nonlinear functional optimization
  methods.

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Mobile Functional Validation Agent
Send
Mobile Agent
Create
User Interface
User Agent

As Service Correct
Correct Service
Jump
Bs Service Correct
Incorrect
Incorrect
MA
MA
MA
Interface Agent
Machine C, D, E, ...
Interface Agent
Computing Server A
Computing Server B
Machine A
C, D, E, ..
Machine B
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Future work and open questions

• Integrate functional validation into grid
  computing infrastructure as a standard grid
  service.
• Extend to other situations described(like
  zero-knowledge proofs, etc.).
• Formulate functional validation problems into
  more appropriate mathematical models.
• Explore solutions for more difficult and
  complicated functional validation situations.
• Thanks!!