A Novel Strategy for Solving the Stochastic Point Location Problem Using a Hierarchical Searching Scheme

Yazidi, Anis; Granmo, Ole‐Christoffer; Oommen, B. John; Goodwin, Morten

doi:10.1109/tcyb.2014.2303712

Cited by 31 publications

(29 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution involves partitioning the line in a hierarchical tree-like manner, and moving to relatively distant points, as characterized by those along the path of the tree. The solution proposed in [18] is an order of magnitude faster than classical SPL solution [8]; however, it works under the premise that p is constant and larger than the golden ratio conjugate. Generalizing the latter solution to the SRF problem is currently being investigated, although it is far from trivial.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Solving Stochastic Root-Finding with adaptive d-ary search

Yazidi

Oommen

2015

2015 IEEE International Conference on Evolving and Adaptive Intelligent Systems (EAIS)

Self Cite

View full text Add to dashboard Cite

Abstract-The most fundamental problem encountered in the field of stochastic optimization, is the Stochastic Root Finding (SRF) problem where the task is to locate an unknown point x * for which g(x * ) = 0 for a given function g that can only be observed in the presence of noise [13]. The vast majority of the state-of-the-art solutions to the SRF problem involve the theory of stochastic approximation. The premise of the latter family of algorithms is to operate by means of so-called "smallstep" processes that explore the search space in a conservative manner. Using this paradigm, the point investigated at any time instant is in the proximity of the point investigated at the previous time instant, rendering the convergence towards the optimal point, x * , to be sluggish. The unfortunate thing about such a search paradigm is that although g() contains information using which large sections of the search space can be eliminated, this information is unutilized. This paper provides a pioneering and novel scheme to discover and utilize this information. Our solution recursively shrinks the search space by, at least, a factor of 2d 3 at each epoch, where d ≥ 2 is a user-defined parameter of the algorithm. This enhances the convergence significantly. Conceptually, this is achieved through a subtle re-formulation of SRF problem in terms of a continuous-space generalization of the Stochastic Point Location (SPL) problem originally proposed by Oommen in [8]. Our scheme is based, in part, on the Continuous Point Location with Adaptive d-ary Search (CPL-AdS), originally presented in [12]. The solution to the CPL-AdS [12], however, is not applicable in our particular domain because of the inherent asymmetry of the SRF problem. Our solution invokes a CPLAdS-like solution to partition the search interval into d subintervals, evaluates the location of the unknown root x * with respect to these sub-intervals using learning automata, and prunes the search space in each iteration by eliminating at least one partition. Our scheme, the CPL-AdS algorithm for SRF, denoted as SRF-AdS, is shown to converge to the unknown root x * with an arbitrary large degree of accuracy, i.e., with a probability as close to unity as desired. Unlike the classical formulation of the SPL problem proposed by Oommen et al [8], [12], in our setting, the probability, p, of the "environment" suggesting an accurate response is non-constant. In fact, the latter probability depends of the point x being examined and the region that is a candidate to be pruned. The fact that p is not constant renders the analysis much more involved than in [12]. The decision rules for pruning are also different from those encountered when p is constant [12].

show abstract

Section: Discussionmentioning

confidence: 99%

“…• Recently Yazidi et al [18] proposed a hierarchical searching scheme for solving the SPL problem. The solution involves partitioning the line in a hierarchical tree-like manner, and of moving to relatively distant points, as characterized by those along the path of the tree.…”

Section: Legacy Spl Solutionsmentioning

confidence: 99%

Solving Stochastic Root-Finding with adaptive d-ary search

Yazidi

Oommen

2015

2015 IEEE International Conference on Evolving and Adaptive Intelligent Systems (EAIS)

Self Cite

View full text Add to dashboard Cite

show abstract

“…The traditional stochastic environment [1], [2], [4]- [8] will inform the learning mechanism to go in a correct direction with a probability, p, and a wrong direction with a probability q = 1 − p. For example, when the current guess of the learning algorithm or mechanism is λ(n)(λ(n) < λ * ), the environment will tell the learning 1 We followed the assumption used in the existing literatures on SPL [1], [2], [5], [7], [8], [29] that the unknown point is in the interval [0, 1]. In fact, this assumption can be easily extended by using monotonic one-to-one mapping to transform the given interval from [0, 1] to [a, b].…”

Section: B Triple Level Stochastic Point Location Problemmentioning

confidence: 99%

“…Generally speaking, the relationship between LA and SPL has been discussed in [29], which pointed out that SPL actually generalized LA strategy for the situation that the optimal action is selected from an infinite set: LA tries to learn the optimal action, defined as what the action can maximize the reward received from the environment, while in the SPL problem the learning mechanism is trying to locate an unknown point on a real interval. The above investigations can also be applied to distinguish the algorithm proposed in this paper from that in [30] and [31].…”

Section: B Triple Level Stochastic Point Location Problemmentioning

confidence: 99%

“…Recently, a hierarchical stochastic searching on the line solution was introduced and demonstrated with faster convergence speed than the CPL-ATS and CPL-AdS strategies [29], which was also found to be able to locate the unknown dynamic point. 2) Another severe limitation of the works reported in [1], [2], [5], [7]- [8], and [29] is that the learning algorithm only accepts two moving directions, i.e., right or left, but the possibility of staying unmoved, which is usually happening in practical applications, has been rarely considered. 3) Lastly, all the solutions presented in [1], [2], [5], [7], and [8] only deal with the stationary environment, which, of course, is not the case in real applications.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Random Walk-Based Solution to Triple Level Stochastic Point Location Problem

Jiang

Huang

2016

IEEE Trans. Cybern.

View full text Add to dashboard Cite

This paper considers the stochastic point location (SPL) problem as a learning mechanism trying to locate a point on a real line via interacting with a random environment. Compared to the stochastic environment in the literatures that confines the learning mechanism to moving in two directions, i.e., left or right, this paper introduces a general triple level stochastic environment which not only tells the learning mechanism to go left or right, but also informs it to stay unmoved. It is easy to understand, as we will prove in this paper, that the environment reported in the previous literatures is just a special case of the triple level environment. And a new learning algorithm, named as random walk-based triple level learning algorithm, is proposed to locate an unknown point under this new type of environment. In order to examine the performance of this algorithm, we divided the triple level SPL problems into four distinguished scenarios by the properties of the unknown point and the stochastic environment, and proved that even under the triple level nonstationary environment and the convergence condition having not being satisfied for some time, which are rarely considered in existing SPL problems, the proposed learning algorithm is still working properly whenever the unknown point is static or evolving with time. Extensive experiments validate our theoretical analyses and demonstrate that the proposed learning algorithms are quite effective and efficient.

show abstract

Application‐Oriented Learning Automata

2023

Learning Automata and Their Applications to Intelligent Systems

View full text Add to dashboard Cite

A Novel Strategy for Solving the Stochastic Point Location Problem Using a Hierarchical Searching Scheme

Cited by 31 publications

References 47 publications

Solving Stochastic Root-Finding with adaptive d-ary search

Solving Stochastic Root-Finding with adaptive d-ary search

Random Walk-Based Solution to Triple Level Stochastic Point Location Problem

Application‐Oriented Learning Automata

Contact Info

Product

Resources

About