Solving Two-Person Zero-Sum Stochastic Games With Incomplete Information Using Learning Automata With Artificial Barriers.

Learning automata (LA) with artificially absorbing barriers was a completely new horizon of research in the 1980s (Oommen, 1986). These new machines yielded properties that were previously unknown. More recently, absorbing barriers have been introduced in continuous estimator algorithms so that the proofs could follow a martingale property, as opposed to monotonicity (Zhang et al., 2014), (Zhang et al., 2015). However, the applications of LA with artificial barriers are almost nonexistent. In that regard, this article is pioneering in that it provides effective and accurate solutions to an extremely complex application domain, namely that of solving two-person zero-sum stochastic games that are provided with incomplete information. LA have been previously used (Sastry et al., 1994) to design algorithms capable of converging to the game's Nash equilibrium under limited information. Those algorithms have focused on the case where the saddle point of the game exists in a pure strategy. However, the majority of the LA algorithms used for games are absorbing in the probability simplex space, and thus, they converge to an exclusive choice of a single action. These LA are thus unable to converge to other mixed Nash equilibria when the game possesses no saddle point for a pure strategy. The pioneering contribution of this article is that we propose an LA solution that is able to converge to an optimal mixed Nash equilibrium even though there may be no saddle point when a pure strategy is invoked. The scheme, being of the linear reward-inaction ( LR-I ) paradigm, is in and of itself, absorbing. However, by incorporating artificial barriers, we prevent it from being "stuck" or getting absorbed in pure strategies. Unlike the linear reward- ϵ penalty ( LR-ϵP ) scheme proposed by Lakshmivarahan and Narendra almost four decades ago, our new scheme achieves the same goal with much less parameter tuning and in a more elegant manner. This article includes the nontrial proofs of the theoretical results characterizing our scheme and also contains experimental verification that confirms our theoretical findings.

The Hierarchical Discrete Pursuit Learning Automaton: A Novel Scheme With Fast Convergence and Epsilon-Optimality.

Since the early 1960s, the paradigm of learning automata (LA) has experienced abundant interest. Arguably, it has also served as the foundation for the phenomenon and field of reinforcement learning (RL). Over the decades, new concepts and fundamental principles have been introduced to increase the LA's speed and accuracy. These include using probability updating functions, discretizing the probability space, and using the "Pursuit" concept. Very recently, the concept of incorporating "structure" into the ordering of the LA's actions has improved both the speed and accuracy of the corresponding hierarchical machines, when the number of actions is large. This has led to the ϵ -optimal hierarchical continuous pursuit LA (HCPA). This article pioneers the inclusion of all the above-mentioned phenomena into a new single LA, leading to the novel hierarchical discretized pursuit LA (HDPA). Indeed, although the previously proposed HCPA is powerful, its speed has an impediment when any action probability is close to unity, because the updates of the components of the probability vector are correspondingly smaller when any action probability becomes closer to unity. We propose here, the novel HDPA, where we infuse the phenomenon of discretization into the action probability vector's updating functionality, and which is invoked recursively at every stage of the machine's hierarchical structure. This discretized functionality does not possess the same impediment, because discretization prohibits it. We demonstrate the HDPA's robustness and validity by formally proving the ϵ -optimality by utilizing the moderation property. We also invoke the submartingale characteristic at every level, to prove that the action probability of the optimal action converges to unity as time goes to infinity. Apart from the new machine being ϵ -optimal, the numerical results demonstrate that the number of iterations required for convergence is significantly reduced for the HDPA, when compared to the state-of-the-art HCPA scheme.

Achieving Fair Load Balancing by Invoking a Learning Automata-Based Two-Time-Scale Separation Paradigm.

In this article, we consider the problem of load balancing (LB), but, unlike the approaches that have been proposed earlier, we attempt to resolve the problem in a fair manner (or rather, it would probably be more appropriate to describe it as an ϵ -fair manner because, although the LB can, probably, never be totally fair, we achieve this by being "as close to fair as possible"). The solution that we propose invokes a novel stochastic learning automaton (LA) scheme, so as to attain a distribution of the load to a number of nodes, where the performance level at the different nodes is approximately equal and each user experiences approximately the same Quality of the Service (QoS) irrespective of which node that he/she is connected to. Since the load is dynamically varying, static resource allocation schemes are doomed to underperform. This is further relevant in cloud environments, where we need dynamic approaches because the available resources are unpredictable (or rather, uncertain) by virtue of the shared nature of the resource pool. Furthermore, we prove here that there is a coupling involving LA's probabilities and the dynamics of the rewards themselves, which renders the environments to be nonstationary. This leads to the emergence of the so-called property of "stochastic diminishing rewards." Our newly proposed novel LA algorithm ϵ -optimally solves the problem, and this is done by resorting to a two-time-scale-based stochastic learning paradigm. As far as we know, the results presented here are of a pioneering sort, and we are unaware of any comparable results.

The Hierarchical Continuous Pursuit Learning Automation: A Novel Scheme for Environments With Large Numbers of Actions.

Although the field of learning automata (LA) has made significant progress in the past four decades, the LA-based methods to tackle problems involving environments with a large number of actions is, in reality, relatively unresolved. The extension of the traditional LA to problems within this domain cannot be easily established when the number of actions is very large. This is because the dimensionality of the action probability vector is correspondingly large, and so, most components of the vector will soon have values that are smaller than the machine accuracy permits, implying that they will never be chosen. This paper presents a solution that extends the continuous pursuit paradigm to such large-actioned problem domains. The beauty of the solution is that it is hierarchical, where all the actions offered by the environment reside as leaves of the hierarchy. Furthermore, at every level, we merely require a two-action LA that automatically resolves the problem of dealing with arbitrarily small action probabilities. In addition, since all the LA invoke the pursuit paradigm, the best action at every level trickles up toward the root. Thus, by invoking the property of the "max" operator, in which the maximum of numerous maxima is the overall maximum, the hierarchy of LA converges to the optimal action. This paper describes the scheme and formally proves its ϵ -optimal convergence. The results presented here can, rather trivially, be extended for the families of discretized and Bayesian pursuit LA too. This paper also reports extensive experimental results (including for environments having 128 and 256 actions) that demonstrate the power of the scheme and its computational advantages. As far as we know, there are no comparable pursuit-based results in the field of LA. In some cases, the hierarchical continuous pursuit automaton requires less than 18% of the number of iterations than the benchmark LR-I scheme, which is, by all metrics, phenomenal.

A Conclusive Analysis of the Finite-Time Behavior of the Discretized Pursuit Learning Automaton.

This paper deals with the finite-time analysis (FTA) of learning automata (LA), which is a topic for which very little work has been reported in the literature. This is as opposed to the asymptotic steady-state analysis for which there are, probably, scores of papers. As clarified later, unarguably, the FTA of Markov chains, in general, and of LA, in particular, is far more complex than the asymptotic steady-state analysis. Such an FTA provides rigid bounds for the time required for the LA to attain to a given convergence accuracy. We concentrate on the FTA of the Discretized Pursuit Automaton (DPA), which is probably one of the fastest and most accurate reported LA. Although such an analysis was carried out many years ago, we record that the previous work is flawed. More specifically, in all brevity, the flaw lies in the wrongly "derived" monotonic behavior of the LA after a certain number of iterations. Rather, we claim that the property should be invoked is the submartingale property. This renders the proof to be much more involved and deep. In this paper, we rectify the flaw and reestablish the FTA based on such a submartingale phenomenon. More importantly, from the derived analysis, we are able to discover and clarify, for the first time, the underlying dilemma between the DPA's exploitation and exploration properties. We also nontrivially confirm the existence of the optimal learning rate, which yields a better comprehension of the DPA itself.

On Solving the Problem of Identifying Unreliable Sensors Without a Knowledge of the Ground Truth: The Case of Stochastic Environments.

The purpose of this paper is to propose a solution to an extremely pertinent problem, namely, that of identifying unreliable sensors (in a domain of reliable and unreliable ones) without any knowledge of the ground truth. This fascinating paradox can be formulated in simple terms as trying to identify stochastic liars without any additional information about the truth. Though apparently impossible, we will show that it is feasible to solve the problem, a claim that is counter-intuitive in and of itself. One aspect of our contribution is to show how redundancy can be introduced, and how it can be effectively utilized in resolving this paradox. Legacy work and the reported literature (for example, in the so-called weighted majority algorithm) have merely addressed assessing the reliability of a sensor by comparing its reading to the ground truth either in an online or an offline manner. Unfortunately, the fundamental assumption of revealing the ground truth cannot be always guaranteed (or even expected) in many real life scenarios. While some extensions of the Condorcet jury theorem [9] can lead to a probabilistic guarantee on the quality of the fused process, they do not provide a solution to the unreliable sensor identification problem. The essence of our approach involves studying the agreement of each sensor with the rest of the sensors, and not comparing the reading of the individual sensors with the ground truth-as advocated in the literature. Under some mild conditions on the reliability of the sensors, we can prove that we can, indeed, filter out the unreliable ones. Our approach leverages the power of the theory of learning automata (LA) so as to gradually learn the identity of the reliable and unreliable sensors. To achieve this, we resort to a team of LA, where a distinct automaton is associated with each sensor. The solution provided here has been subjected to rigorous experimental tests, and the results presented are, in our opinion, both novel and conclusive.

Learning-automaton-based online discovery and tracking of spatiotemporal event patterns.

Discovering and tracking of spatiotemporal patterns in noisy sequences of events are difficult tasks that have become increasingly pertinent due to recent advances in ubiquitous computing, such as community-based social networking applications. The core activities for applications of this class include the sharing and notification of events, and the importance and usefulness of these functionalities increase as event sharing expands into larger areas of one's life. Ironically, instead of being helpful, an excessive number of event notifications can quickly render the functionality of event sharing to be obtrusive. Indeed, any notification of events that provides redundant information to the application/user can be seen to be an unnecessary distraction. In this paper, we introduce a new scheme for discovering and tracking noisy spatiotemporal event patterns, with the purpose of suppressing reoccurring patterns, while discerning novel events. Our scheme is based on maintaining a collection of hypotheses, each one conjecturing a specific spatiotemporal event pattern. A dedicated learning automaton (LA)--the spatiotemporal pattern LA (STPLA)--is associated with each hypothesis. By processing events as they unfold, we attempt to infer the correctness of each hypothesis through a real-time guided random walk. Consequently, the scheme that we present is computationally efficient, with a minimal memory footprint. Furthermore, it is ergodic, allowing adaptation. Empirical results involving extensive simulations demonstrate the superior convergence and adaptation speed of STPLA, as well as an ability to operate successfully with noise, including both the erroneous inclusion and omission of events. An empirical comparison study was performed and confirms the superiority of our scheme compared to a similar state-of-the-art approach. In particular, the robustness of the STPLA to inclusion as well as to omission noise constitutes a unique property compared to other related approaches. In addition, the results included, which involve the so-called " presence sharing" application, are both promising and, in our opinion, impressive. It is thus our opinion that the proposed STPLA scheme is, in general, ideal for improving the usefulness of event notification and sharing systems, since it is capable of significantly, robustly, and adaptively suppressing redundant information.

Modeling the "learning process" of the teacher in a tutorial-like system using learning automata.

Unlike the field of tutorial systems, where a real-life student interacts and learns from a software system, our research focuses on a new philosophy in which no entity needs to be a real-life individual. Such systems are termed as tutorial-like systems, and research in this field endeavors to model every component of the system using an appropriate learning model [in our case, a learning automaton (LA)].1 While models for the student, the domain, the teacher, etc., have been presented elsewhere, the aim of this paper is to present a new approach to model how the teacher, in this paradigm, of our tutorial-like system "learns and improves his "teaching skills" while being himself an integral component of the system. We propose to model the "learning process" of the teacher by using a higher level LA, referred to as the metateacher, whose task is to assist the teacher himself. Ultimately, the intention is that the latter can communicate the teaching material to the student(s) in a manner customized to the particular student's ability and progress. In short, the teacher will infer the progress of the student and initiate a strategy by which he can "custom-communicate" the material to each individual student. The results that we present in a simulated environment validate the model for the teacher and for the metateacher. The use of the latter can be seen to significantly improve the teaching abilities of the teacher.

On utilizing association and interaction concepts for enhancing microaggregation in secure statistical databases.

This paper presents a possibly pioneering endeavor to tackle the Microaggregation Techniques (MATs) in secure statistical databases by resorting to the principles of associative neural networks (NNs). The prior art has improved the available solutions to the MAT by incorporating proximity information, and this approach is done by recursively reducing the size of the data set by excluding points that are farthest from the centroid and points that are closest to these farthest points. Thus, although the method is extremely effective, arguably, it uses only the proximity information while ignoring the mutual interaction between the records. In this paper, we argue that interrecord relationships can be quantified in terms of the following two entities: 1) their "association" and 2) their "interaction." This case means that records that are not necessarily close to each other may still be "grouped," because their mutual interaction, which is quantified by invoking transitive-closure-like operations on the latter entity, could be significant, as suggested by the theoretically sound principles of NNs. By repeatedly invoking the interrecord associations and interactions, the records are grouped into sizes of cardinality " k," where k is the security parameter in the algorithm. Our experimental results, which are done on artificial data and benchmark real-life data sets, demonstrate that the newly proposed method is superior to the state of the art not only based on the Information Loss (IL) perspective but also when it concerns a criterion that involves a combination of the IL and the Disclosure Risk (DR).

Solving multiconstraint assignment problems using learning automata.

This paper considers the NP-hard problem of object assignment with respect to multiple constraints: assigning a set of elements (or objects) into mutually exclusive classes (or groups), where the elements which are "similar" to each other are hopefully located in the same class. The literature reports solutions in which the similarity constraint consists of a single index that is inappropriate for the type of multiconstraint problems considered here and where the constraints could simultaneously be contradictory. This feature, where we permit possibly contradictory constraints, distinguishes this paper from the state of the art. Indeed, we are aware of no learning automata (or other heuristic) solutions which solve this problem in its most general setting. Such a scenario is illustrated with the static mapping problem, which consists of distributing the processes of a parallel application onto a set of computing nodes. This is a classical and yet very important problem within the areas of parallel computing, grid computing, and cloud computing. We have developed four learning-automata (LA)-based algorithms to solve this problem: First, a fixed-structure stochastic automata algorithm is presented, where the processes try to form pairs to go onto the same node. This algorithm solves the problem, although it requires some centralized coordination. As it is desirable to avoid centralized control, we subsequently present three different variable-structure stochastic automata (VSSA) algorithms, which have superior partitioning properties in certain settings, although they forfeit some of the scalability features of the fixed-structure algorithm. All three VSSA algorithms model the processes as automata having first the hosting nodes as possible actions; second, the processes as possible actions; and, third, attempting to estimate the process communication digraph prior to probabilistically mapping the processes. This paper, which, we believe, comprehensively reports the pioneering LA solutions to this problem, unequivocally demonstrates that LA can play an important role in solving complex combinatorial and integer optimization problems.

Modeling a student-classroom interaction in a tutorial-like system using learning automata.

Almost all of the learning paradigms used in machine learning, learning automata (LA), and learning theory, in general, use the philosophy of a Student (learning mechanism) attempting to learn from a teacher. This paradigm has been generalized in a myriad of ways, including the scenario when there are multiple teachers or a hierarchy of mechanisms that collectively achieve the learning. In this paper, we consider a departure from this paradigm by allowing the Student to be a member of a classroom of Students, where, for the most part, we permit each member of the classroom not only to learn from the teacher(s) but also to "extract" information from any of his fellow Students. This paper deals with issues concerning the modeling, decision-making process, and testing of such a scenario within the LA context. The main result that we show is that a weak learner can actually benefit from this capability of utilizing the information that he gets from a superior colleague-if this information transfer is done appropriately. As far as we know, the whole concept of Students learning from both a teacher and from a classroom of Students is novel and unreported in the literature. The proposed Student-classroom interaction has been tested for numerous strategies and for different environments, including the established benchmarks, and the results show that Students can improve their learning by interacting with each other. For example, for some interaction strategies, a weak Student can improve his learning by up to 73% when interacting with a classroom of Students, which includes Students of various capabilities. In these interactions, the Student does not have a priori knowledge of the identity or characteristics of the Students who offer their assistance.

Random early detection for congestion avoidance in wired networks: a discretized pursuit learning-automata-like solution.

In this paper, we present a learning-automata-like The reason why the mechanism is not a pure LA, but rather why it yet mimics one, will be clarified in the body of this paper. (LAL) mechanism for congestion avoidance in wired networks. Our algorithm, named as LAL Random Early Detection (LALRED), is founded on the principles of the operations of existing RED congestion-avoidance mechanisms, augmented with a LAL philosophy. The primary objective of LALRED is to optimize the value of the average size of the queue used for congestion avoidance and to consequently reduce the total loss of packets at the queue. We attempt to achieve this by stationing a LAL algorithm at the gateways and by discretizing the probabilities of the corresponding actions of the congestion-avoidance algorithm. At every time instant, the LAL scheme, in turn, chooses the action that possesses the maximal ratio between the number of times the chosen action is rewarded and the number of times that it has been chosen. In LALRED, we simultaneously increase the likelihood of the scheme converging to the action, which minimizes the number of packet drops at the gateway. Our approach helps to improve the performance of congestion avoidance by adaptively minimizing the queue-loss rate and the average queue size. Simulation results obtained using NS2 establish the improved performance of LALRED over the traditional RED methods which were chosen as the benchmarks for performance comparison purposes.

Adachi-like chaotic neural networks requiring linear-time computations by enforcing a tree-shaped topology.

The Adachi neural network (AdNN) is a fascinating neural network (NN) which has been shown to possess chaotic properties, and to also demonstrate associative memory (AM) and pattern recognition (PR) characteristics. Variants of the AdNN have also been used to obtain other PR phenomena, and even blurring. An unsurmountable problem associated with the AdNN and the variants referred to above is that all of them require a quadratic number of computations. This is essentially because the NNs in each case are completely connected graphs. In this paper, we consider how the computations can be significantly reduced by merely using a linear number of computations. To achieves this, we extract from the original completely connected graph one of its spanning trees. We then address the problem of computing the weights for this spanning tree. This is done in such a manner that the modified tree-based NN has approximately the same input-output characteristics, and thus the new weights are themselves calculated using a gradient-based algorithm. By a detailed experimental analysis, we show that the new linear-time AdNN-like network possesses chaotic and PR properties for different settings. As far as we know, such a tree-based AdNN has not been reported, and the results given here are novel.

Achieving microaggregation for secure statistical databases using fixed-structure partitioning-based learning automata.

We consider the microaggregation problem (MAP) that involves partitioning a set of individual records in a microdata file into a number of mutually exclusive and exhaustive groups. This problem, which seeks for the best partition of the microdata file, is known to be NP-hard and has been tackled using many heuristic solutions. In this paper, we present the first reported fixed-structure-stochastic-automata-based solution to this problem. The newly proposed method leads to a lower value of the information loss (IL), obtains a better tradeoff between the IL and the disclosure risk (DR) when compared with state-of-the-art methods, and leads to a superior value of the scoring index, which is a criterion involving a combination of the IL and the DR. The scheme has been implemented, tested, and evaluated for different real-life and simulated data sets. The results clearly demonstrate the applicability of learning automata to the MAP and its ability to yield a solution that obtains the best tradeoff between IL and DR when compared with the state of the art.

A solution to the stochastic point location problem in metalevel nonstationary environments.

This paper reports the first known solution to the stochastic point location (SPL) problem when the environment is nonstationary. The SPL problem involves a general learning problem in which the learning mechanism (which could be a robot, a learning automaton, or, in general, an algorithm) attempts to learn a "parameter," for example, lambda*, within a closed interval. However, unlike the earlier reported results, we consider the scenario when the learning is to be done in a nonstationary setting. For each guess, the environment essentially informs the mechanism, possibly erroneously (i.e., with probability p), which way it should move to reach the unknown point. Unlike the results available in the literature, we consider the fascinating case when the point sought for is itself stochastically moving (which is modeled as follows). The environment communicates with an intermediate entity (referred to as the teacher/oracle) about the point itself, i.e., advising where it should go. The mechanism that searches for the point in turn receives responses from the teacher/oracle, which directs how it should move. Therefore, the point itself, in the overall setting, is moving, i.e., delivering possibly incorrect information about its location to the teacher/oracle. This in turn means that the "environment" is itself nonstationary, which implies that the advice of the teacher/oracle is both uncertain and changing with time-rendering the problem extremely fascinating. The heart of the strategy we propose involves discretizing the space and performing a controlled random walk on this space. Apart from deriving some analytic results about our solution, we also report the simulation results that demonstrate the power of the scheme, and state some potential applications.

On using prototype reduction schemes to optimize kernel-based fisher discriminant analysis.

Fisher's linear discriminant analysis (LDA) is a traditional dimensionality reduction method that has been proven to be successful for decades. Numerous variants, such as the kernel-based Fisher discriminant analysis (KFDA), have been proposed to enhance the LDA's power for nonlinear discriminants. Although effective, the KFDA is computationally expensive, since the complexity increases with the size of the data set. In this correspondence, we suggest a novel strategy to enhance the computation for an entire family of the KFDAs. Rather than invoke the KFDA for the entire data set, we advocate that the data be first reduced into a smaller representative subset using a prototype reduction scheme and that the dimensionality reduction be achieved by invoking a KFDA on this reduced data set. In this way, data points that are ineffective in the dimension reduction and classification can be eliminated to obtain a significantly reduced kernel matrix K without degrading the performance. Our experimental results demonstrate that the proposed mechanism dramatically reduces the computation time without sacrificing the classification accuracy for artificial and real-life data sets.

Desynchronizing a chaotic pattern recognition neural network to model inaccurate perception.

The usual goal of modeling natural and artificial perception involves determining how a system can extract the object that it perceives from an image that is noisy. The "inverse" of this problem is one of modeling how even a clear image can be perceived to be blurred in certain contexts. To our knowledge, there is no solution to this in the literature other than for an oversimplified model in which the true image is garbled with noise by the perceiver himself. In this paper, we propose a chaotic model of pattern recognition (PR) for the theory of "blurring." This paper, which is an extension to a companion paper demonstrates how one can model blurring from the view point of a chaotic PR system. Unlike the companion paper in which a chaotic PR system extracts the pattern from the input, in this case, we show that even without the inclusion of additional noise, perception of an object can be "blurred" if the dynamics of the chaotic system are modified. We thus propose a formal model and present an analysis using the Lyapunov exponents and the Routh-Hurwitz criterion. We also demonstrate experimentally the validity of our model by using a numeral data set. A byproduct of this model is the theoretical possibility of desynchronization of the periodic behavior of the brain (as a chaotic system), rendering us the possibility of predicting, controlling, and annulling epileptic behavior.

Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation.

This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.

Stochastic automata-based estimators for adaptively compressing files with nonstationary distributions.

This correspondence shows that learning automata techniques, which have been useful in developing weak estimators, can be applied to data compression applications in which the data distributions are nonstationary. The adaptive coding scheme utilizes stochastic learning-based weak estimation techniques to adaptively update the probabilities of the source symbols, and this is done without resorting to either maximum likelihood, Bayesian, or sliding-window methods. The authors have incorporated the estimator in the adaptive Fano coding scheme and in an adaptive entropy-based scheme that "resembles" the well-known arithmetic coding. The empirical results obtained for both of these adaptive methods are obtained on real-life files that possess a fair degree of nonstationarity. From these results, it can be seen that the proposed schemes compress nearly 10% more than their respective adaptive methods that use maximum-likelihood estimator-based estimates.

Parameter learning from stochastic teachers and stochastic compulsive liars.

This paper considers a general learning problem akin to the field of learning automata (LA) in which the learning mechanism attempts to learn from a stochastic teacher or a stochastic compulsive liar. More specifically, unlike the traditional LA model in which LA attempts to learn the optimal action offered by the Environment (also here called the "Oracle"), this paper considers the problem of the learning mechanism (robot, an LA, or in general, an algorithm) attempting to learn a "parameter" within a closed interval. The problem is modeled as follows: The learning mechanism is trying to locate an unknown point on a real interval by interacting with a stochastic Environment through a series of informed guesses. For each guess, the Environment essentially informs the mechanism, possibly erroneously (i.e., with probability p), which way it should move to reach the unknown point. When the probability of a correct response is p > 0.5, the Environment is said to be informative, and thus the case of learning from a stochastic teacher. When this probability p < 0.5, the Environment is deemed deceptive, and is called a stochastic compulsive liar. This paper describes a novel learning strategy by which the unknown parameter can be learned in both environments. These results are the first reported results, which are applicable to the latter scenario. The most significant contribution of this paper is that the proposed scheme is shown to operate equally well, even when the learning mechanism is unaware of whether the Environment ("Oracle") is informative or deceptive. The learning strategy proposed herein, called CPL-AdS, partitions the search interval into d subintervals, evaluates the location of the unknown point with respect to these subintervals using fast-converging E-optimal LRI LA, and prunes the search space in each iteration by eliminating at least one partition. The CPL-AdS algorithm is shown to provably converge to the unknown point with an arbitrary degree of accuracy with probability as close to unity as desired. Comprehensive experimental results confirm the fast and accurate convergence of the search for a wide range of values for the Environment's feedback accuracy parameter p, and thus has numerous potential applications.