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It is shown that under standard hypotheses, if stochastic approximationiterates 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) isprovided. Further, estimates on lock-in probability, i.e., the probability ofconvergence to a specific attractor of the o.d.e. limit given that the iteratesvisit its domain of attraction, and sample complexity, i.e., the number ofsteps needed to be within a prescribed neighborhood of the desired limit setwith a prescribed probability, are also provided. The latter improvesignificantly upon existing results in that they require a much weakercondition on the martingale difference noise.

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