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On stochastic approximation algorithms for classes of PAC learning problems.

N V Rao1, V R Uppuluri, E M Oblow

  • 1Center for Eng. Syst. Adv. Res., Oak Ridge Nat. Lab., TN.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|January 1, 1997
PubMed
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Stochastic approximation methods offer new algorithms for Probably Approximately Correct (PAC) learning problems. These methods utilize artificial neural networks and martingale inequalities to ensure error bounds for efficient machine learning.

Area of Science:

  • Machine Learning
  • Computational Statistics
  • Artificial Intelligence

Background:

  • The Probably Approximately Correct (PAC) learning model is a foundational framework in computational learning theory.
  • Classical stochastic approximation methods have been explored for optimization problems but their application to PAC learning requires further investigation.
  • Efficient algorithms are needed to address the complexities of PAC learning, especially in high-dimensional spaces.

Purpose of the Study:

  • To develop and analyze algorithms for solving various formulations of the PAC learning problem.
  • To explore the use of nonpolynomial units, such as artificial neural networks, within stochastic approximation frameworks for PAC learning.
  • To derive conditions on sample sizes necessary for guaranteeing error bounds in PAC learning algorithms.

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Main Methods:

  • Application of classical stochastic approximation methods to PAC learning formulations on the domain [0,1](d).
  • Design of algorithms employing networks of nonpolynomial units, including artificial neural networks, under smoothness conditions.
  • Utilizing martingale inequalities to derive bounds on the required sample sizes for achieving desired error guarantees.

Main Results:

  • Demonstrated that stochastic approximation methods can yield effective algorithms for PAC learning.
  • Proposed simple, yet powerful, algorithms for specific PAC learning problems using neural network architectures.
  • Established theoretical conditions on sample sizes crucial for ensuring the performance and error bounds of the proposed algorithms.

Conclusions:

  • Stochastic approximation provides a viable approach for developing algorithms in PAC learning.
  • Artificial neural networks integrated with stochastic approximation show promise for solving complex PAC learning tasks.
  • The derived conditions on sample sizes offer practical guidance for implementing these learning algorithms effectively.