An innovative fractional order LMS based on variable initial value and gradient order

Cheng, Songsong; Wei, Yiheng; Chen, Yuquan; Li, Yan; Wang, Yong

doi:10.1016/j.sigpro.2016.11.026

Cited by 81 publications

(24 citation statements)

References 36 publications

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“…It is noticed that the rate of convergence and the steady state error increases for higher fractional orders e.g., 0.9. The impact of fractional order on the convergence speed and accuracy was explored in [62] using the fractional order in the range of (1, 1.5).…”

Section: ) Selection Of the Fractional Order (F R )mentioning

confidence: 99%

Design of Momentum Fractional Stochastic Gradient Descent for Recommender Systems

Khan

Zubair²,

Alquhayz

et al. 2019

IEEE Access

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The demand for recommender systems in E-commerce industry has increased tremendously. Efficient recommender systems are being proposed by different E-business companies with the intention to give users accurate and most relevant recommendation of products from huge amount of information. To improve the performance of recommender systems, various stochastic variants of gradient descent based algorithms have been reported. The scalability requirement of recommender systems needs algorithms with fast convergence to generate recommendations of specific items. Using the concepts of fractional calculus, an efficient variant of the stochastic gradient descent (SGD) was developed for fast convergence. Such fractional SGD (F-SGD) is further accelerated by adding a momentum term, thus termed as momentum fractional stochastic gradient descent (mF-SGD). The proposed mF-SGD method is shown to offer improved estimation accuracy and convergence rate, as compared to F-SGD and standard momentum SGD for different proportions of previous gradients, fractional orders, learning rates and number of features.

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Section: ) Selection Of the Fractional Order (F R )mentioning

confidence: 99%

Design of Momentum Fractional Stochastic Gradient Descent for Recommender Systems

Khan

Zubair²,

Alquhayz

et al. 2019

IEEE Access

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“…In fact, fractional order has been developed for 300 years and used to solve many kinds of problems such as control applications and systems' theory [15][16][17]. In comparison with the traditional integer order algorithm, the fractional order algorithm has more design freedom and potential to obtain better convergence performance [18,19].…”

Section: Introductionmentioning

confidence: 99%

Distributed Policy Evaluation with Fractional Order Dynamics in Multiagent Reinforcement Learning

Wang²,

Mao

et al. 2021

Security and Communication Networks

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The main objective of multiagent reinforcement learning is to achieve a global optimal policy. It is difficult to evaluate the value function with high-dimensional state space. Therefore, we transfer the problem of multiagent reinforcement learning into a distributed optimization problem with constraint terms. In this problem, all agents share the space of states and actions, but each agent only obtains its own local reward. Then, we propose a distributed optimization with fractional order dynamics to solve this problem. Moreover, we prove the convergence of the proposed algorithm and illustrate its effectiveness with a numerical example.

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“…On the other hand, thanks to that many systems can be described accurately with the introduction of fractional calculus, fractional systems have attracted much attention from engineering and physics fields. Besides, the application of fractional calculus in control systems also has rapidly development, especially in stability analysis [15,16], controller design [17,18], adaptive filtering [19,20], etc. An important class of theoretical and practical problems is how to obtain the exact state when state variables cannot be measured directly.…”

Section: Introductionmentioning

confidence: 99%

Fractional central difference Kalman filter with unknown prior information

et al. 2019

Self Cite

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In this paper, a generalized fractional central difference Kalman filter for nonlinear discrete fractional dynamic systems is proposed. Based on the Stirling interpolation formula, the presented algorithm can be implemented as no derivatives are needed. Besides, in order to estimate the state with unknown prior information, a maximum a posteriori principle based adaptive fractional central difference Kalman filter is derived. The adaptive algorithm can estimate the noise statistics and system state simultaneously. The unbiasedness of the proposed algorithm is analyzed. Several numerical examples demonstrate the accuracy and effectiveness of the two Kalman filters.

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An innovative fractional order LMS based on variable initial value and gradient order

Cited by 81 publications

References 36 publications

Design of Momentum Fractional Stochastic Gradient Descent for Recommender Systems

Design of Momentum Fractional Stochastic Gradient Descent for Recommender Systems

Distributed Policy Evaluation with Fractional Order Dynamics in Multiagent Reinforcement Learning

Fractional central difference Kalman filter with unknown prior information

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