We propose stochastic gradient algorithm based on exponentiated cost functions that employ higher order moments of the chosen error. Recently, such algorithms based on exponential dependence of squared of the error have attracted a lot of attention. It has been felt that such algorithms have only been tested in the Gaussian noise environment. Motivated by the performance of the least-mean-fourth algorithm in sub-Gaussian environments, we make use of the same strategy to come up with a new algorithm with superior convergence and steady-state performance. Simulations show promising results.
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