Learning Automata (LA) is a popular decision making mechanism to “determine the optimal action out of a set of allowable actions” (Agache and Oommen, IEEE Trans Syst Man Cybern-Part B Cybern 2002(6): 738–749, 2002). The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself (Thathachar and Sastry, IEEE Trans Syst Man Cybern-Part B Cybern 32(6): 711–722, 2002). Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems (Goodwin and Yazidi 2016). In this paper, we propose a novel classifier based on the theory of LA. The classification problem is formulated as a deterministic optimization problem involving a team of LA that operate collectively to optimize an objective function. Although many LA algorithms have been devised in the literature, those LA schemes are not able to solve deterministic optimization problems as they suppose that the environment is stochastic. In this paper, we develop a novel pursuit LA which can be seen as the counterpart of the family of pursuit LA developed for stochastic environments (Agache and Oommen, IEEE Trans Syst Man Cybern Part B Cybern 32(6): 738–749, 2002). While classical pursuit LA are able to pursue the action with the highest reward estimate, our pursuit LA rather pursues the collection of actions that yield the highest performance. The theoretical analysis of the pursuit scheme does not follow classical LA proofs and can pave the way towards more schemes where LA can be applied to solve deterministic optimization problems. When applied to classification, the essence of our scheme is to search for a separator in the feature space by imposing a LA based random walk in a grid system. To each node in the gird we attach an LA, whose actions are the choice of the edges forming the separator. The walk is self-enclosing, i.e., a new random walk is started whenever the walker returns to starting node forming a closed classification path yielding a multiedged polygon. In our approach, the different LA attached at the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygons, we perform classification by labelling items encircled by a polygon as part of a class using ray casting function. Seen from a methodological perspective, PolyPursuit-LA has appealing properties compared to SVM. In fact, unlike PolyPursuit-LA, the SVM performance is dependent on the right choice of kernel function (e.g. Linear Kernel, Gaussian Kernel)— which is considered a “black art”. PolyPursuit-LA can find arbitrarily complex separators in the feature space. Experimental results from both synthetic and real-life data show that our scheme is able to perfectly separate both simple and complex patterns outperforming existing classifiers, including polynomial and linear SVM, without the need of any “kernel trick”. We believe that the results are impressive given the simplicity of PolyPursuit-LA compared to other approaches such as SVM.

学习自动机（LA）是一种流行的决策机制，可以“从一组允许的动作中确定最佳动作”（Agache和Oommen，IEEE Trans Syst Man Cyber​​n-Part B Cyber​​n 2002（6）：738–749，2002） 。基于自动机的学习的显着特征是，在参数空间上定义的概率分布空间中而不是在参数空间本身中搜索优化参数向量（Thathachar和Sastry，IEEE Trans Syst Man Cyber​​n-Part B Cyber​​n 32（6）：711–722，2002）。最近，Goodwin和Yazidi率先使用蚁群优化（ACO）解决分类问题（Goodwin和Yazidi 2016）。在本文中，我们基于洛杉矶理论提出了一种新颖的分类器。分类问题被公式化为确定性优化问题，涉及一个LA团队，这些团队共同运作以优化目标函数。尽管在文献中已经设计了许多LA算法，但是这些LA方案假定环境是随机的，因此无法解决确定性优化问题。在本文中，我们开发了一种新型的追随LA，可以将其视为为随机环境开发的追逐LA系列的对应产品（Agache和Oommen，IEEE Trans Syst Man Cyber​​n Part B Cyber​​n 32（6）：738–749，2002）。尽管经典的追逐LA能够以最高的报酬估算来追随行动，但我们的追逐LA宁可追寻产生最高绩效的行动。追踪方案的理论分析没有遵循经典的LA证明，可以为更多可以将LA用于解决确定性优化问题的方案铺平道路。当应用于分类时，我们方案的本质是通过在网格系统中施加基于LA的随机游走来在特征空间中搜索分隔符。我们在网格的每个节点上附加一个LA，LA的作用是选择形成分隔符的边。步行是自封闭的，即，只要步行者返回到起始节点形成闭合的分类路径并产生多边多边形，就会开始新的随机步行。在我们的方法中 连接在不同节点上的不同LA会搜索最能包围并分隔每个类别的多边形。基于获得的多边形，我们通过使用光线投射功能将多边形所包围的项标记为类的一部分来进行分类。从方法论的角度来看，与SVM相比，PolyPursuit-LA具有吸引人的特性。实际上，与PolyPursuit-LA不同，SVM的性能取决于正确选择内核功能（例如，线性内核，高斯内核），这被认为是“妖术”。PolyPursuit-LA可以在特征空间中找到任意复杂的分隔符。综合数据和实际数据的实验结果表明，我们的方案能够完美地分离简单和复杂模式，其性能优于现有分类器，包括多项式和线性SVM，无需任何“内核技巧”。我们相信，与其他方法（例如SVM）相比，PolyPursuit-LA的简单性可以使结果令人印象深刻。