A modified second-order SPSA optimization algorithm for finite samples
نویسندگان
چکیده
We propose a modification to the simultaneous perturbation stochastic approximation (SPSA) methods based on the comparisons made between the firstand second-order SPSA (1SPSA and 2SPSA) algorithms from the perspective of loss function Hessian. At finite iterations, the accuracy of the algorithm depends on the matrix conditioning of the loss function Hessian. The error of 2SPSA algorithm for a loss function with an ill-conditioned Hessian is greater than the one with a well-conditioned Hessian. On the other hand, the 1SPSA algorithm is less sensitive to the matrix conditioning of loss function Hessians. The modified 2SPSA (M2SPSA) eliminates the error amplification caused by the inversion of an ill-conditioned Hessian. This leads to significant improvements in its algorithm efficiency in problems with an ill-conditioned Hessian matrix. Asymptotically, the efficiency analysis shows that M2SPSA is also superior to 2SPSA in a large parameter domain. It is shown that the ratio of the mean square errors for M2SPSA to 2SPSA is always less than one except for a perfectly conditioned Hessian or for an asymptotically optimal setting of the gain sequence. Copyright # 2002 John Wiley & Sons, Ltd.
منابع مشابه
Second Order Sliding Mode Control With Finite Time Convergence
In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...
متن کاملA probabilistic constrained nonlinear optimization framework to optimize RED parameters
The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz., queue weight (wq), marking probability (maxp), minimum threshold (minth) and maximum threshold (maxth) is not analytically available. Moreover, the precise dependence between the RED average queue length and its parameters is...
متن کاملSPSA-NC: simultaneous perturbation stochastic approximation localization based on neighbor confidence
Accuracy is still the greatest challenge in the wireless sensor network localization efforts. Several diverse factors can give rise to localization errors. Modeling such diverse influencing factors to deliver a single, reasonably simple and practical solution is a difficult task. In order to address the problem of location inaccuracy, we propose a comparatively simple and ingenious approach, wh...
متن کاملGlobal Optimization via SPSA
A desire with iterative optimization techniques is that the algorithm reaches the global optimum rather than get stranded at a local optimum value. In this paper, we examine the theoretical and numerical global convergence properties of a certain “gradient free” stochastic approximation algorithm called “SPSA,” that has performed well in complex optimization problems. We establish two theorems ...
متن کاملCoarse-to-Fine Registration of Remote Sensing Optical Images using SIFT and SPSA Optimization
Sub-pixel accuracy is the vital requirement of remote sensing optical image registration. For this purpose, a coarse-to-fine registration algorithm is proposed to register the remote sensing optical images. The coarse registration operation is performed by the scale-invariant feature transform (SIFT) approach with an outlier removal method. The outliers are removed by the Random sample consensu...
متن کامل