However, one might argue that this analysis might not allow for sufficient differentiation between tasks. To address this concern, we expanded our evaluation to the entire MMLU benchmark. This enabled a comparable assessment of task similarity, akin to our earlier experiments.

Adaptability has been regarded as a central feature in the foundation models, enabling them to effectively acclimate to unseen downstream tasks. Parameter-efficient fine-tuning methods such as celebrated LoRA facilitate efficient adaptation of large foundation models using labeled, high-quality and generally scarce task data. To mitigate data scarcity in fine-tuning of foundation models, we propose to leverage task similarity across multiple downstream users. Intuitively, users with similar tasks must be able to assist each other in boosting the effective fine-tuning data size. We propose Collaborative Low-Rank Adaptation, or CoLoRA, which exploits task similarity to collaboratively and efficiently fine-tune personalized foundation models. The main idea in CoLoRA is to train one shared adapter capturing underlying task similarities across all tasks, and personalized adapters tailored to user-specific tasks. We theoretically study CoLoRA on heterogeneous linear regression and provide provable guarantees for ground truth recovery. We also conduct several natural language experiments with varying task similarity, which further demonstrate that when trained together with similar tasks, individual performances are significantly boosted.

Conversely, the opposite scenario is relatively benign.

Multi-agent reinforcement learning (MARL) has primarily focused on solving a single task in isolation, while in practice the environment is often evolving, leaving many related tasks to be solved. In this paper, we investigate the benefits of meta-learning in solving multiple MARL tasks collectively. We establish the first line of theoretical results for meta-learning in a wide range of fundamental MARL settings, including learning Nash equilibria in two-player zero-sum Markov games and Markov potential games, as well as learning coarse correlated equilibria in general-sum Markov games. Under natural notions of task similarity, we show that meta-learning achieves provable sharper convergence to various game-theoretical solution concepts than learning each task separately. As an important intermediate step, we develop multiple MARL algorithms with initialization-dependent convergence guarantees. Such algorithms integrate optimistic policy mirror descents with stage-based value updates, and their refined convergence guarantees (nearly) recover the best known results even when a good initialization is unknown. To our best knowledge, such results are also new and might be of independent interest. We further provide numerical simulations to corroborate our theoretical findings.

In this paper, we study the Tiered Reinforcement Learning setting, a parallel transfer learning framework, where the goal is to transfer knowledge from the low-tier (source) task to the high-tier (target) task to reduce the exploration risk of the latter while solving the two tasks in parallel. Unlike previous work, we do not assume the low-tier and high-tier tasks share the same dynamics or reward functions, and focus on robust knowledge transfer without prior knowledge on the task similarity. We identify a natural and necessary condition called the ``Optimal Value Dominance'' for our objective. Under this condition, we propose novel online learning algorithms such that, for the high-tier task, it can achieve constant regret on partial states depending on the task similarity and retain near-optimal regret when the two tasks are dissimilar, while for the low-tier task, it can keep near-optimal without making sacrifice. Moreover, we further study the setting with multiple low-tier tasks, and propose a novel transfer source selection mechanism, which can ensemble the information from all low-tier tasks and allow provable benefits on a much larger state-action space.

Continual learning of partially similar tasks poses a challenge for artificial neural networks, as task similarity presents both an opportunity for knowledge transfer and a risk of interference and catastrophic forgetting.However, it remains unclear how task similarity in input features and readout patterns influences knowledge transfer and forgetting, as well as how they interact with common algorithms for continual learning.Here, we develop a linear teacher-student model with latent structure and show analytically that high input feature similarity coupled with low readout similarity is catastrophic for both knowledge transfer and retention. Conversely, the opposite scenario is relatively benign. Our analysis further reveals that task-dependent activity gating improves knowledge retention at the expense of transfer, while task-dependent plasticity gating does not affect either retention or transfer performance at the over-parameterized limit. In contrast, weight regularization based on the Fisher information metric significantly improves retention, regardless of task similarity, without compromising transfer performance. Nevertheless, its diagonal approximation and regularization in the Euclidean space are much less robust against task similarity. We demonstrate consistent results in a permuted MNIST task with latent variables. Overall, this work provides insights into when continual learning is difficult and how to mitigate it.

The reward for each arm is random according to a fixed distribution, and the agent's goal is to maximize