In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained stochastic optimization problems, with the constraints originating mainly from model assumptions that define a trade-off between complexity and performance. This trade-off is closely related to over-fitting, generalization capacity, and robustness to noise and adversarial attacks, and depends on both the structure and complexity of the model, as well as the properties of the optimization methods used. We develop an online prototype-based learning algorithm based on annealing optimization that is formulated as an online gradient-free stochastic approximation algorithm. The learning model can be viewed as an interpretable and progressively growing competitive-learning neural network model to be used for supervised, unsupervised, and reinforcement learning. The annealing nature of the algorithm contributes to minimal hyper-parameter tuning requirements, poor local minima prevention, and robustness with respect to the initial conditions. At the same time, it provides online control over the performance-complexity trade-off by progressively increasing the complexity of the learning model as needed, through an intuitive bifurcation phenomenon. Finally, the use of stochastic approximation enables the study of the convergence of the learning algorithm through mathematical tools from dynamical systems and control, and allows for its integration with reinforcement learning algorithms, constructing an adaptive state-action aggregation scheme.
翻译:在这项工作中,我们引入了一种旨在满足计算资源有限、稳健性和可解释性得到优先考虑的应用需要的学习模式;学习问题可以作为限制的随机优化问题提出,其制约因素主要来自界定复杂性和性能之间的权衡的模型假设。这种权衡与过度适应、普遍化能力和对噪音和对抗性攻击的稳健性密切相关,并取决于模型的结构和复杂性以及所用优化方法的特性。我们开发了基于自觉优化的在线原型学习算法,该原型算法是作为在线无梯度随机近似算法拟订的。学习模式可被视为一种可解释的和日益增长的竞争性学习神经网络模型,用于监管、不超超强、对噪音和对抗性攻击的稳健性,取决于模型的结构和复杂性,以及所用优化方法的特性。与此同时,我们开发了一种基于自上层优化的在线控制,即以无梯度超梯度的随机近似近似近似近似性排序法。学习模型,通过学习双向性递增压性递增性递增性递增性矩阵,从而得以学习模式的升级。