We identify a natural and necessary condition called the "Optimal

However, BO suffers from the so called'cold start' problem [

Learning systems often expand their ambient features or latent representations over time, embedding earlier representations into larger spaces with limited new latent structure. We study transfer learning for structured matrix estimation under simultaneous growth of the ambient dimension and the intrinsic representation, where a well-estimated source task is embedded as a subspace of a higher-dimensional target task. We propose a general transfer framework in which the target parameter decomposes into an embedded source component, low-dimensional low-rank innovations, and sparse edits, and develop an anchored alternating projection estimator that preserves transferred subspaces while estimating only low-dimensional innovations and sparse modifications. We establish deterministic error bounds that separate target noise, representation growth, and source estimation error, yielding strictly improved rates when rank and sparsity increments are small. We demonstrate the generality of the framework by applying it to two canonical problems. For Markov transition matrix estimation from a single trajectory, we derive end-to-end theoretical guarantees under dependent noise. For structured covariance estimation under enlarged dimensions, we provide complementary theoretical analysis in the appendix and empirically validate consistent transfer gains.

Instead of considering "online" and "continual" learning as inconvenient constraints to avoid, in

Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for \emph{active representation learning}, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve $\varepsilon$-excess risk on target scales with $(k^*)^2 ||v^*||_2^2 \varepsilon^{-2}$ where $k^*$ is the effective dimension of the target and $||v^*||_2^2 \in (0,1]$ represents the connection between source and target space. Compared to the passive one, this can save up to $\frac{1}{d_W}$ of sample complexity, where $d_W$ is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by 20%-70%.

In recent years, Multi-Agent Reinforcement Learning (MARL) techniques have made significant strides in achieving high asymptotic performance in single task. However, there has been limited exploration of model transferability across tasks. Training a model from scratch for each task can be time-consuming and expensive, especially for large-scale Multi-Agent Systems. Therefore, it is crucial to develop methods for generalizing the model across tasks. Considering that there exist task-independent subtasks across MARL tasks, a model that can decompose such subtasks from the source task could generalize to target tasks. However, ensuring true task-independence of subtasks poses a challenge. In this paper, we propose to \textbf{d}ecompose a \textbf{t}ask in\textbf{to} a series of \textbf{g}eneralizable \textbf{s}ubtasks (DT2GS), a novel framework that addresses this challenge by utilizing a scalable subtask encoder and an adaptive subtask semantic module. We show that these components endow subtasks with two properties critical for task-independence: avoiding overfitting to the source task and maintaining consistent yet scalable semantics across tasks. Empirical results demonstrate that DT2GS possesses sound zero-shot generalization capability across tasks, exhibits sufficient transferability, and outperforms existing methods in both multi-task and single-task problems.