One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the last decades, a substantial amount of work has been devoted to design estimators for the unknown function and to study their convergence to the optimal predictor, also characterizing the learning rate. These results typically rely on stationary assumptions where input locations are drawn from a probability distribution that does not change in time. In this work, we consider kernel-based ridge regression and derive convergence conditions under non stationary distributions, addressing also cases where stochastic adaption may happen infinitely often. This includes the important exploration-exploitation problems where e.g. a set of agents/robots has to monitor an environment to reconstruct a sensorial field and their movements rules are continuously updated on the basis of the acquired knowledge on the field and/or the surrounding environment.

翻译：机器学习中的一个核心主题是从稀疏且含噪声的数据中进行函数估计。例如在监督学习中，训练集元素由输入位置与输出响应构成的配对组成。过去数十年间，大量研究致力于设计未知函数的估计量，并研究其收敛到最优预测器的特性，同时刻画学习速率。这些结果通常基于平稳性假设，即输入位置服从一个不随时间变化的概率分布。本文考虑基于核的岭回归方法，推导非平稳分布下的收敛条件，并处理随机适应可能无限发生的情形。这包括重要的探索-利用问题，例如一组智能体/机器人需要监测环境以重构传感场，其移动规则根据对场域及/或周边环境的认知不断更新。