Kernel-based function learning in dynamic and non stationary environments
This work addresses function learning in dynamic settings, such as exploration-exploitation in robotics, but is incremental as it extends existing kernel methods to non-stationary assumptions.
The paper tackles the problem of kernel-based ridge regression in non-stationary environments, deriving convergence conditions for cases where distributions change over time, including infinite stochastic adaptations.
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.