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

Author's accepted manuscript© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.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 reduce...acceptedVersio

The design of absorbing Bayesian pursuit algorithms and the formal analyses of their ε-optimality

The fundamental phenomenon that has been used to enhance the convergence speed of learning automata (LA) is that of incorporating the running maximum likelihood (ML) estimates of the action reward probabilities into the probability updating rules for selecting the actions. The frontiers of this field have been recently expanded by replacing the ML estimates with their corresponding Bayesian counterparts that incorporate the properties of the conjugate priors. These constitute the Bayesian pursuit algorithm (BPA), and the discretized Bayesian pursuit algorithm. Although these algorithms have been designed and efficiently implemented, and are, arguably, the fastest and most accurate LA reported in the literature, the proofs of their ϵϵ-optimal convergence has been unsolved. This is precisely the intent of this paper. In this paper, we present a single unifying analysis by which the proofs of both the continuous and discretized schemes are proven. We emphasize that unlike the ML-based pursuit schemes, the Bayesian schemes have to not only consider the estimates themselves but also the distributional forms of their conjugate posteriors and their higher order moments—all of which render the proofs to be particularly challenging. As far as we know, apart from the results themselves, the methodologies of this proof have been unreported in the literature—they are both pioneering and novel

On the Theory and Applications of Hierarchical Learning Automata and Object Migration Automata

Paper III, IV and VIII are excluded due to copyright.The paradigm of Artificial Intelligence (AI) and the sub-group of Machine Learning (ML) have attracted exponential interest in our society in recent years. The domain of ML contains numerous methods, and it is desirable (and in one sense, mandatory) that these methods are applicable and valuable to real-life challenges. Learning Automata (LA) is an intriguing and classical direction within ML. In LA, non-human agents can find optimal solutions to various problems through the concept of learning. The LA instances learn through Agent-Environment interactions, where advantageous behavior is rewarded, and disadvantageous behavior is penalized. Consequently, the agent eventually, and hopefully, learns the optimal action from a set of actions. LA has served as a foundation for Reinforcement Learning (RL), and the field of LA has been studied for decades. However, many improvements can still be made to render these algorithms to be even more convenient and effective. In this dissertation, we record our research contributions to the design and applications within the field of LA. Our research includes novel improvements to the domain of hierarchical LA, major advancements to the family of Object Migration Automata (OMA) algorithms, and a novel application of LA, where it was utilized to solve challenges in a mobile radio communication system. More specifically, we introduced the novel Hierarchical Discrete Pursuit Automaton (HDPA), which significantly improved the state of the art in terms of effectiveness for problems with high accuracy requirements, and we mathematically proved its ϵ-optimality. In addition, we proposed the Action Distribution Enhanced (ADE) approach to hierarchical LA schemes which significantly reduced the number of iterations required before the machines reached convergence. The existing schemes in the OMA paradigm, which are able to solve partitioning problems, could only solve problems with equally-sized partitions. Therefore, we proposed two novel methods that could handle unequally-sized partitions. In addition, we rigorously summarized the OMA domain, outlined its potential benefits to society, and listed further development cases for future researchers in the field. With regard to applications, we proposed an OMA-based approach to the grouping and power allocation in Non-orthogonal Multiple Access (NOMA) systems, demonstrating the applicability of the OMA and its advantage in solving fairly complicated stochastic problems. The details of these contributions and their published scientific impacts will be summarized in this dissertation, before we present some of the research contributions in their entirety.publishedVersio

Mungojerrie:Linear-Time Objectives in Model-Free Reinforcement Learning

Mungojerrie is an extensible tool that provides a framework to translate linear-time objectives into reward for reinforcement learning (RL). The tool provides convergent RL algorithms for stochastic games, reference implementations of existing reward translations for ω -regular objectives, and an internal probabilistic model checker for ω -regular objectives. This functionality is modular and operates on shared data structures, which enables fast development of new translation techniques. Mungojerrie supports finite models specified in PRISM and ω -automata specified in the HOA format, with an integrated command line interface to external linear temporal logic translators. Mungojerrie is distributed with a set of benchmarks for ω -regular objectives in RL.</p

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

Author's accepted manuscript.© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.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.acceptedVersio

Multi-agent persistent surveillance under temporal logic constraints

This thesis proposes algorithms for the deployment of multiple autonomous agents for persistent surveillance missions requiring repeated, periodic visits to regions of interest. Such problems arise in a variety of domains, such as monitoring ocean conditions like temperature and algae content, performing crowd security during public events, tracking wildlife in remote or dangerous areas, or watching traffic patterns and road conditions. Using robots for surveillance is an attractive solution to scenarios in which fixed sensors are not sufficient to maintain situational awareness. Multi-agent solutions are particularly promising, because they allow for improved spatial and temporal resolution of sensor information. In this work, we consider persistent monitoring by teams of agents that are tasked with satisfying missions specified using temporal logic formulas. Such formulas allow rich, complex tasks to be specified, such as "visit regions A and B infinitely often, and if region C is visited then go to region D, and always avoid obstacles." The agents must determine how to satisfy such missions according to fuel, communication, and other constraints. Such problems are inherently difficult due to the typically infinite horizon, state space explosion from planning for multiple agents, communication constraints, and other issues. Therefore, computing an optimal solution to these problems is often infeasible. Instead, a balance must be struck between computational complexity and optimality. This thesis describes solution methods for two main classes of multi-agent persistent surveillance problems. First, it considers the class of problems in which persistent surveillance goals are captured entirely by TL constraints. Such problems require agents to repeatedly visit a set of surveillance regions in order to satisfy their mission. We present results for agents solving such missions with charging constraints, with noisy observations, and in the presence of adversaries. The second class of problems include an additional optimality criterion, such as minimizing uncertainty about the location of a target or maximizing sensor information among the team of agents. We present solution methods and results for such missions with a variety of optimality criteria based on information metrics. For both classes of problems, the proposed algorithms are implemented and evaluated via simulation, experiments with robots in a motion capture environment, or both

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 ( $L_{R-I}$ ) 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-εpenalty ( $L_{R-ε P}$ ) 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.acceptedVersio