On the convergence, lock-in probability and sample complexity of stochastic approximation

Sameer Kamal

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arXiv · 1007.4684

On the convergence, lock-in probability and sample complexity of stochastic approximation

Sameer Kamal

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Abstract

It is shown that under standard hypotheses, if stochastic approximation iterates remain tight, they converge with probability one to what their o.d.e. limit suggests. A simple test for tightness (and therefore a.s. convergence) is provided. Further, estimates on lock-in probability, i.e., the probability of convergence to a specific attractor of the o.d.e. limit given that the iterates visit its domain of attraction, and sample complexity, i.e., the number of steps needed to be within a prescribed neighborhood of the desired limit set with a prescribed probability, are also provided. The latter improve significantly upon existing results in that they require a much weaker condition on the martingale difference noise.

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Sameer Kamal. 2010-07-27. On the convergence, lock-in probability and sample complexity of stochastic approximation. https://arxiv.org/abs/1007.4684

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