Training Large Language Models (LLMs) poses significant memory challenges, making low-rank adaptation methods an attractive solution. Previously, Low-Rank Adaptation (LoRA) addressed this by adding a trainable low-rank matrix to the frozen pre-trained weights in each layer, reducing the number of trainable parameters and optimizer states. GaLore, which compresses the gradient matrix instead of the weight matrix, has demonstrated superior performance to LoRA with faster convergence and reduced memory consumption. Despite their empirical success, the performance of these methods has not been fully understood or explained theoretically. In this paper, we analyze the optimization landscapes of LoRA, GaLore, and full-rank methods, revealing that GaLore benefits from fewer spurious local minima and a larger region that satisfies the \pl, a variant of Polyak-Łojasiewicz (PL) condition, leading to faster convergence. Our analysis leads to a novel method, GaRare, which further improves GaLore by using gradient random projection to reduce computational overhead. Practically, GaRare achieves strong performance in both pre-training and fine-tuning tasks, offering a more efficient approach to large-scale model adaptation.

Extracting temporally extended skills can significantly improve the efficiency of reinforcement learning (RL) by breaking down complex decision-making problems with sparse rewards into simpler subtasks and enabling more effective credit assignment. However, existing abstraction methods either discover skills in an unsupervised manner, which often lacks semantic information and leads to erroneous or scattered skill extraction results, or require substantial human intervention. In this work, we propose to leverage the extensive knowledge in pretrained Vision-Language Models (VLMs) to progressively guide the latent space after vector quantization to be more semantically meaningful through relabeling each skill. This approach, termed **V**ision-l**an**guage model guided **T**emporal **A**bstraction (**VanTA**), facilitates the discovery of more interpretable and task-relevant temporal segmentations from offline data without the need for extensive manual intervention or heuristics. By leveraging the rich information in VLMs, our method can significantly outperform existing offline RL approaches that depend only on limited training data. From a theory perspective, we demonstrate that stronger internal sequential correlations within each sub-task, induced by VanTA, effectively reduces suboptimality in policy learning. We validate the effectiveness of our approach through extensive experiments on diverse environments, including Franka Kitchen, Minigrid, and Crafter. These experiments show that our method surpasses existing approaches in long-horizon offline reinforcement learning scenarios with both proprioceptive and visual observations.

Learning a high-quality transition model is of great importance for sequential decision-making tasks, especially in offline settings. Nevertheless, the complex behaviors of transition dynamics in real-world environments pose challenges for the standard forward models because of their inductive bias towards smooth regressors, conflicting with the inherent nature of transitions such as discontinuity or large curvature. In this work, we propose to model the transition probability implicitly through a scalar-value energy function, which enables not only flexible distribution prediction but also capturing complex transition behaviors. The Energy-based Transition Models (ETM) are shown to accurately fit the discontinuous transition functions and better generalize to out-of-distribution transition data. Furthermore, we demonstrate that energy-based transition models improve the evaluation accuracy and significantly outperform other off-policy evaluation methods in DOPE benchmark. Finally, we show that energy-based transition models also benefit reinforcement learning and outperform prior offline RL algorithms in D4RL Gym-Mujoco tasks.

Combining offline and online reinforcement learning (RL) techniques is indeed crucial for achieving efficient and safe learning where data acquisition is expensive. Existing methods replay offline data directly in the online phase, resulting in a significant challenge of data distribution shift and subsequently causing inefficiency in online fine-tuning. To address this issue, we introduce an innovative approach, Energy-guided DIffusion Sampling (EDIS), which utilizes a diffusion model to extract prior knowledge from the offline dataset and employs energy functions to distill this knowledge for enhanced data generation in the online phase. The theoretical analysis demonstrates that EDIS exhibits reduced suboptimality compared to solely utilizing online data or directly reusing offline data. EDIS is a plug-in approach and can be combined with existing methods in offline-to-online RL setting. By implementing EDIS to off-the-shelf methods Cal-QL and IQL, we observe a notable 20% average improvement in empirical performance on MuJoCo, AntMaze, and Adroit environments. Code is available at https://github.com/liuxhym/EDIS.

Teaching dimension (TD) is a fundamental theoretical property for understanding machine teaching algorithms. It measures the sample complexity of teaching a target hypothesis to a learner. The TD of linear learners has been studied extensively, whereas the results of teaching non-linear learners are rare. A recent result investigates the TD of polynomial and Gaussian kernel learners. Unfortunately, the theoretical bounds therein show that the TD is high when teaching those non-linear learners. Inspired by the fact that regularization can reduce the learning complexity in machine learning, a natural question is whether the similar fact happens in machine teaching. To answer this essential question, this paper proposes a unified theoretical framework termed STARKE to analyze the TD of regularized kernel learners. On the basis of STARKE, we derive a generic result of any type of kernels. Furthermore, we disclose that the TD of regularized linear and regularized polynomial kernel learners can be strictly reduced. For regularized Gaussian kernel learners, we reveal that, although their TD is infinite, their epsilon-approximate TD can be exponentially reduced compared with that of the unregularized learners. The extensive experimental results of teaching the optimization-based learners verify the theoretical findings.

AutoML aims at best configuring learning systems automatically. It contains core subtasks of algorithm selection and hyper-parameter tuning. Previous approaches considered searching in the joint hyper-parameter space of all algorithms, which forms a huge but redundant space and causes an inefficient search. We tackle this issue in acascaded algorithm selectionway, which contains an upper-level process of algorithm selection and a lower-level process of hyper-parameter tuning for algorithms. While the lower-level process employs ananytimetuning approach, the upper-level process is naturally formulated as a multi-armed bandit, deciding which algorithm should be allocated one more piece of time for the lower-level tuning. To achieve the goal of finding the best configuration, we propose theExtreme-Region Upper Confidence Bound(ER-UCB) strategy. Unlike UCB bandits that maximize the mean of feedback distribution, ER-UCB maximizes the extreme-region of feedback distribution. We first consider stationary distributions and propose the ER-UCB-S algorithm that has$O(K\ln n)$regret upper bound with$K$arms and$n$trials. We then extend to non-stationary settings and propose the ER-UCB-N algorithm that has$O(Kn^\nu)$regret upper bound, where$\frac{2}{3}<\nu <1$. Finally, empirical studies on synthetic and AutoML tasks verify the effectiveness of ER-UCB-S/N by their outperformance in corresponding settings.

In reinforcement learning, experience replay stores past samples for further reuse. Prioritized sampling is a promising technique to better utilize these samples. Previous criteria of prioritization include TD error, recentness and corrective feedback, which are mostly heuristically designed. In this work, we start from the regret minimization objective, and obtain an optimal prioritization strategy for Bellman update that can directly maximize the return of the policy. The theory suggests that data with higher hindsight TD error, better on-policiness and more accurate Q value should be assigned with higher weights during sampling. Thus most previous criteria only consider this strategy partially. We not only provide theoretical justifications for previous criteria, but also propose two new methods to compute the prioritization weight, namely ReMERN and ReMERT. ReMERN learns an error network, while ReMERT exploits the temporal ordering of states. Both methods outperform previous prioritized sampling algorithms in challenging RL benchmarks, including MuJoCo, Atari and Meta-World.