Domain Generalization by Marginal Transfer Learning

In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This problem arises in several applications where data distributions fluctuate because of environmental, technical, or other sources of variation. We introduce a formal framework for DG, and argue that it can be viewed as a kind of supervised learning problem by augmenting the original feature space with the marginal distribution of feature vectors. While our framework has several connections to conventional analysis of supervised learning algorithms, several unique aspects of DG require new methods of analysis. This work lays the learning theoretic foundations of domain generalization, building on our earlier conference paper where the problem of DG was introduced Blanchard et al., 2011. We present two formal models of data generation, corresponding notions of risk, and distribution-free generalization error analysis. By focusing our attention on kernel methods, we also provide more quantitative results and a universally consistent algorithm. An efficient implementation is provided for this algorithm, which is experimentally compared to a pooling strategy on one synthetic and three real-world data sets

Lifelong Bandit Optimization: No Prior and No Regret

In practical applications, machine learning algorithms are often repeatedly applied to problems with similar structure over and over again. We focus on solving a sequence of bandit optimization tasks and develop LiBO, an algorithm which adapts to the environment by learning from past experience and becoming more sample-efficient in the process. We assume a kernelized structure where the kernel is unknown but shared across all tasks. LiBO sequentially meta-learns a kernel that approximates the true kernel and simultaneously solves the incoming tasks with the latest kernel estimate. Our algorithm can be paired with any kernelized bandit algorithm and guarantees oracle optimal performance, meaning that as more tasks are solved, the regret of LiBO on each task converges to the regret of the bandit algorithm with oracle knowledge of the true kernel. Naturally, if paired with a sublinear bandit algorithm, LiBO yields a sublinear lifelong regret. We also show that direct access to the data from each task is not necessary for attaining sublinear regret. The lifelong problem can thus be solved in a federated manner, while keeping the data of each task private.Comment: 32 pages, 6 figures, preprin

Progressive growing of self-organized hierarchical representations for exploration

Designing agent that can autonomously discover and learn a diversity of structures and skills in unknown changing environments is key for lifelong machine learning. A central challenge is how to learn incrementally representations in order to progressively build a map of the discovered structures and re-use it to further explore. To address this challenge, we identify and target several key functionalities. First, we aim to build lasting representations and avoid catastrophic forgetting throughout the exploration process. Secondly we aim to learn a diversity of representations allowing to discover a "diversity of diversity" of structures (and associated skills) in complex high-dimensional environments. Thirdly, we target representations that can structure the agent discoveries in a coarse-to-fine manner. Finally, we target the reuse of such representations to drive exploration toward an "interesting" type of diversity, for instance leveraging human guidance. Current approaches in state representation learning rely generally on monolithic architectures which do not enable all these functionalities. Therefore, we present a novel technique to progressively construct a Hierarchy of Observation Latent Models for Exploration Stratification, called HOLMES. This technique couples the use of a dynamic modular model architecture for representation learning with intrinsically-motivated goal exploration processes (IMGEPs). The paper shows results in the domain of automated discovery of diverse self-organized patterns, considering as testbed the experimental framework from Reinke et al. (2019)