A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed num...A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed number of previous noisy function values as a criterion for accepting good and rejecting bad steps.The scheine allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that larger steps will improve the performance.An algorithin with the new adaptive scheme is defined for a general descent direction.The ahnost sure convergence is established.The performance of new algorithm is tested on a set of standard test problems and compared with relevant algorithms.Numerical results support theoretical expectations and verify efficiency of the algorithm regardless of chosen search direction and noise level.Numerical results on probleins arising in machine learning are also presented.Linear regression problem is considered using real data set.The results suggest that the proposed algorithln shows proinise.展开更多
文摘A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed number of previous noisy function values as a criterion for accepting good and rejecting bad steps.The scheine allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that larger steps will improve the performance.An algorithin with the new adaptive scheme is defined for a general descent direction.The ahnost sure convergence is established.The performance of new algorithm is tested on a set of standard test problems and compared with relevant algorithms.Numerical results support theoretical expectations and verify efficiency of the algorithm regardless of chosen search direction and noise level.Numerical results on probleins arising in machine learning are also presented.Linear regression problem is considered using real data set.The results suggest that the proposed algorithln shows proinise.
