A novel technique for stochastic root-finding: Enhancing the search with adaptive d-ary search

Yazidi, Anis; Oommen, B. John

doi:10.1016/j.ins.2017.02.014

Cited by 5 publications

(4 citation statements)

References 33 publications

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“…In this paper, we introduce an adaptive control mechanism to control the mobility of thermocline sensors to improve the link stability in underwater networks. We model the problem as a variant of the SPL problem [14,20,25]. In a similar manner to SPL, the LMA is only allowed to move only into two directions.…”

Section: Resultsmentioning

confidence: 99%

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A pursuit learning solution to underwater communications with limited mobility agents

Bennouri

Yazidi

Berqia

2018

Proceedings of the 2018 Conference on Research in Adaptive and Convergent Systems

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Underwater environments are subject to varying conditions which might degrade the quality of communications. In this paper, we propose an adaptive control mechanism to improve the communication in underwater sensor networks using the theory of Learning Automata (LA). Our LA based solution controls the mobility of thermocline sensors to improve the link stability in underwater networks. The problem is modelled as a variant of the Stochastic Point Location (SPL) problem [14, 20, 25]. The sensor is allowed two directions of movement, either surface or dive, in order to avoid physical phenomena that cause faults. Our proposed scheme constitutes also a contribution to the field of LA and particularly to the SPL problem by resorting to the concept of pursuit LA. In fact, pursuit LA exploits more effectively the information from the environment than traditional LA schemes that are myopic and use merely the last feedback from the environment instead of considering the whole history of the feedback. Experimental results show the performance of our algorithm and its ability to find the optimal sensor position. CCS CONCEPTS • Computing methodologies → Computational control theory; • Applied computing; • Networks → Network components;

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Section: Resultsmentioning

confidence: 99%

“…The SPL has been successfully applied in different domains such as binomial estimation [24], quantile estimation [21,22], stochastic root finding [25] and solving the non-linear stochastic knapsack problem [6,23].…”

Section: Legacy Stochastic Point Location Solutionsmentioning

confidence: 99%

A pursuit learning solution to underwater communications with limited mobility agents

Bennouri

Yazidi

Berqia

2018

Proceedings of the 2018 Conference on Research in Adaptive and Convergent Systems

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“…Yazidi et al [32], proposed a new variant of SPL, to find the root of a stochastic equation, where the equation may have one or more unknowns and the solution is found through a process of iterative search and pruning using an adaptive d-ary search approach. In their approach, they consider a non-constant probability and non-symmetry responses of the "environment", which makes a more accurate and efficient approach to stochastic root-finding problems than in previous cases where probability was assumed to be constant and symmetric.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Probabilistic Tsetlin Machine for Pattern Recognition

Elmisadr,

Belaid,

Yazidi

2023

Preprint

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This article introduces a novel approach, termed the Asymmetric Probabilistic Tsetlin (APT) Machine, which incorporates the Stochastic Point Location (SPL) algorithm with the Asymmetric Steps technique into the Tsetlin Machine (TM). APT introduces stochasticity into the state transitions of Tsetlin Automata (TA) by leveraging the SPL algorithm, thereby enhancing pattern recognition capabilities. To enhance random search processes, we introduced a decaying normal distribution into the procedure. Meanwhile, the Asymmetric Steps approach biases state transition probabilities towards specific input patterns, further elevating operational efficiency. The efficacy of the proposed approach is assessed across diverse benchmark datasets for classification tasks. The performance of APT is compared with traditional machine learning algorithms and other Tsetlin Machine models, including the Asymmetric Tsetlin (AT) Machine, characterized by deterministic rules for Asymmetric transitions, and the Classical Tsetlin (CT) Machine, employing deterministic rules for symmetric transitions. Strikingly, the introduced APT methodology demonstrates highly competitive outcomes compared to established machine learning methods. Notably, both APT and AT exhibit state-of-the-art performance, surpassing the Classical Tsetlin Machine, emphasizing the efficacy of asymmetric models for achieving superior outcomes. Remarkably, APT exhibits even better performance than AT, particularly in handling complex datasets.

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“…In [30], it is proposed to apply the SPL paradigm to solve the stochastic root finding problem which is a well-known stochastic optimization problem. The classical solution to solve this problem is based on stochastic approximation.…”

Section: Introductionmentioning

confidence: 99%

On solving the SPL problem using the concept of probability flux

2019

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The Stochastic Point Location (SPL) problem [20] is a fundamental learning problem that has recently found a lot of research attention. SPL can be summarized as searching for an unknown point in an interval under faulty feedback. The search is performed via a Learning Mechanism (LM) (algorithm) that interacts with a stochastic Environment which in turn informs it about the direction of the search. Since the Environment is stochastic, the guidance for directions could be faulty. The first solution to the SPL problem, which was pioneered two decades ago by Oommen, relies on discretizing the search interval and performing a controlled random walk on it. The state of the random walk at each step is considered to be the estimation of the point location. The convergence of the latter simplistic estimation strategy is proved for an infinite resolution, i.e., infinite memory. However, this strategy yields rather poor accuracy for low discretization resolutions. In this paper, we present two major contributions to the SPL problem. First, we demonstrate that the estimation of the point location can significantly be improved by resorting to the concept of mutual probability flux between neighboring states along the line. Second, we are able to accurately track the position of the optimal point and simultaneously show a method by which we can estimate the error probability characterizing the Environment. Interestingly, learning this error probability of the Environment takes place in tandem with the unknown location estimation. We present and analyze several experiments discussing the weaknesses and strengths of the different methods.

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A novel technique for stochastic root-finding: Enhancing the search with adaptive d-ary search

Cited by 5 publications

References 33 publications

A pursuit learning solution to underwater communications with limited mobility agents

A pursuit learning solution to underwater communications with limited mobility agents

Asymmetric Probabilistic Tsetlin Machine for Pattern Recognition

On solving the SPL problem using the concept of probability flux

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