A one-measurement form of simultaneous perturbation stochastic approximation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has proven very effective for difficult multivariate optimization problems where it is not possible to obtain direct gradient information. As discussed to date, SPSA is based on a highly efficient gradient approximation requiring only two measurements of the loss function independent of the number of parameters being estimated. This note presents a form of SPSA that requires only one function measurement (for any dimension). Theory is presented that identifies the class of problems for which this one-measurement form will be asymptotically superior to the standard two-measurement form.

• Publication year

  1997

• Venue

  at - Automatisierungstechnik

• Publication date

  Unknown publication date

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/S0005-1098(96)00149-5
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• The one-measurement SPSA form uses only one function measurement instead of two.

  Confidence 0.97

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• Theoretical analysis identifies a class of optimization problems for which the one-measurement SPSA form is asymptotically superior to the standard two-measurement form.

  Confidence 0.94

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• A one-measurement form of simultaneous perturbation stochastic approximation is introduced that works for any parameter dimension.

  Confidence 0.98

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review

• asymptotic superiority

  property

  A performance relation in which one algorithm has better limiting behavior than another as iterations grow.

  Aliases: asymptotically superior

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• class of problems

  problem class

  The set of optimization problems for which the stated theoretical condition applies.

  Aliases: problems class

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• function measurement

  measurement

  A single evaluation of the loss function at a chosen parameter setting.

  Aliases: measurement of the loss function, function evaluation

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• one-measurement spsa

  method

  A variant of SPSA that estimates updates using a single function evaluation per iteration.

  Aliases: one-measurement form of SPSA

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• simultaneous perturbation stochastic approximation

  method

  A stochastic optimization method that estimates gradients from simultaneous perturbations of the parameters.

  Aliases: SPSA

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review
• two-measurement spsa

  method

  The standard SPSA variant that estimates updates using two function evaluations per iteration.

  Aliases: standard two-measurement form

  박진우 (dztg5apj7m) extractionB (s683577b42) reviewAnonymous (12632b8b5f) review

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