Direct Preference Optimization (DPO) has emerged as a stable, scalable, and efficient solution for language model alignment. Despite its empirical success, the optimization properties, particularly the impact of samplers on its convergence rates, remain under-explored. In this paper, we provide a rigorous analysis of DPO's convergence rates with different sampling strategies under the exact gradient setting, revealing a surprising separation: uniform sampling achieves $\textbf{linear}$ convergence, while our proposed online sampler achieves $\textbf{quadratic}$ convergence. We further adapt the sampler to practical settings by incorporating posterior distributions and logit mixing, demonstrating improvements over previous methods. For example, it outperforms vanilla DPO by over $7.4$% on Safe-RLHF dataset. Our results not only offer insights into the theoretical understanding of DPO but also pave the way for further algorithm designs.

Web 3.0 is redefining the current Web (Web 2.0) with a focus on data and governance decentralization. The InterPlanetary File System (IPFS) exemplifies this shift. However, it faces a trade-off between decentralization and performance: prior studies have shown IPFS's performance degradations but fail to diagnose root causes or deliver actionable fixes.

The InterPlanetary File System (IPFS) is a pioneering effort for Web 3.0, well-known for its decentralized infrastructure. However, some recent studies have shown that IPFS exhibits a high degree of centralization and has integrated centralized components for improved performance. While this change contradicts the core decentralized ethos of IPFS and introduces risks of hurting the data replication level and thus availability, it also opens some opportunities for better data management and cost savings through deduplication.

Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets. Given recent advances in Large Language Models (LLMs) and their few-shot learning prowess, this paper introduces $\textbf{La}$nguage Models for $\textbf{Mo}$tion Control ($\textbf{LaMo}$), a general framework based on Decision Transformers to effectively use pre-trained Language Models (LMs) for offline RL. Our framework highlights four crucial components: (1) Initializing Decision Transformers with sequentially pre-trained LMs, (2) employing the LoRA fine-tuning method, in contrast to full-weight fine-tuning, to combine the pre-trained knowledge from LMs and in-domain knowledge effectively, (3) using the non-linear MLP transformation instead of linear projections, to generate embeddings, and (4) integrating an auxiliary language prediction loss during fine-tuning to stabilize the LMs and retain their original abilities on languages. Empirical results indicate $\textbf{LaMo}$ achieves state-of-the-art performance in sparse-reward tasks and closes the gap between value-based offline RL methods and decision transformers in dense-reward tasks. In particular, our method demonstrates superior performance in scenarios with limited data samples.

Sequential decision-making algorithms such as reinforcement learning (RL) in real-world scenarios inevitably face environments with partial observability. This paper scrutinizes the effectiveness of a popular architecture, namely Transformers, in Partially Observable Markov Decision Processes (POMDPs) and reveals its theoretical limitations. We establish that regular languages, which Transformers struggle to model, are reducible to POMDPs. This poses a significant challenge for Transformers in learning POMDP-specific inductive biases, due to their lack of inherent recurrence found in other models like RNNs. This paper casts doubt on the prevalent belief in Transformers as sequence models for RL and proposes to introduce a point-wise recurrent structure. The Deep Linear Recurrent Unit (LRU) emerges as a well-suited alternative for Partially Observable RL, with empirical results highlighting the sub-optimal performance of the Transformer and considerable strength of LRU.

Aligning language models (LMs) to human preferences has emerged as a critical pursuit, enabling these models to better serve diverse user needs. Existing methods primarily focus on optimizing LMs for a single reward function, limiting their adaptability to varied objectives. Here, we propose $\textbf{multi-objective decoding~(MOD)}$, a decoding-time algorithm that outputs the next token from a linear combination of predictions of all base models, for any given weighting over different objectives. We exploit a common form among a family of $f$-divergence regularized alignment approaches (such as PPO, DPO, and their variants) to identify a closed-form solution by Legendre transform, and derive an efficient decoding strategy. Theoretically, we show why existing approaches can be sub-optimal even in natural settings and obtain optimality guarantees for our method. Empirical results demonstrate the effectiveness of the algorithm. For example, compared to a parameter-merging baseline, MOD achieves 12.8\% overall reward improvement when equally optimizing towards $3$ objectives. Moreover, we experiment with MOD on combining three fully-finetuned LMs of different model sizes, each aimed at different objectives such as safety, coding, and general user preference. Unlike traditional methods that require careful curation of a mixture of datasets to achieve comprehensive improvement, we can quickly experiment with preference weightings using MOD to find the best combination of models. Our best combination reduces toxicity on Toxigen to nearly 0\% and achieves 7.9--33.3\% improvement across three other metrics ($\textit{i.e.}$, Codex@1, GSM-COT, BBH-COT).

Human hands possess remarkable dexterity and have long served as a source of inspiration for robotic manipulation. In this work, we propose a human $\textbf{H}$and-$\textbf{In}$formed visual representation learning framework to solve difficult $\textbf{Dex}$terous manipulation tasks ($\textbf{H-InDex}$) with reinforcement learning. Our framework consists of three stages: $\textit{(i)}$ pre-training representations with 3D human hand pose estimation, $\textit{(ii)}$ offline adapting representations with self-supervised keypoint detection, and $\textit{(iii)}$ reinforcement learning with exponential moving average BatchNorm. The last two stages only modify $0.36$% parameters of the pre-trained representation in total, ensuring the knowledge from pre-training is maintained to the full extent. We empirically study $\textbf{12}$ challenging dexterous manipulation tasks and find that $\textbf{H-InDex}$ largely surpasses strong baseline methods and the recent visual foundation models for motor control. Code and videos are available at https://yanjieze.com/H-InDex .

This paper presents a novel efficient method for gridless line spectrum estimation problem with single snapshot and sparse signals, namely the gradient descent least squares (GDLS) method. Conventional single snapshot (a.k.a. single measure vector or SMV) line spectrum estimation methods either rely on smoothing techniques that sacrificing the range and/or azimuth resolution, or adopt the sparsity constraint and utilize compressed sensing (CS) method by defining prior grids and resulting in the off-grid problem. Recently emerged atomic norm minimization (ANM) methods achieved gridless SMV line spectrum estimation, but its computational complexity is extremely high; thus it is practically infeasible in real applications with large problem scales. Our proposed GDLS method reformulates the line spectrum estimations problem into a least squares (LS) estimation problem and solves the corresponding objective function via gradient descent algorithm in an iterative fashion with efficiency. The convergence guarantee, computational complexity, as well as performance analysis for evenly distributed antenna array case are discussed in this paper. Numerical simulations show that the proposed GDLS algorithm outperforms the state-of-the-art methods e.g., CS and ANM, in terms of estimation performances. It can completely avoid the off-grid problem, and its computational complexity is significantly lower than ANM. Our method has been tested in tomographic SAR (TomoSAR) imaging applications via simulated and real experiment data. Results show great potential of the proposed method in terms of better cloud point performance and eliminating the gridding effect.

Three-dimensional imaging with tomographic SAR is a hot research topic in the field of SAR. The existing methods usually solve the question based on elevation discretization. When the target point has an off-grid deviation, the accuracy will decrease and the number of spurious points will increase. In this paper, a position-first step-by-step 3D inversion method is proposed. By constructing the observation equation with only an unknown elevation position, the height of the scattering center is directly solved in the continuous domain based on the least square criterion, and then the scattering coefficient is calculated based on the position. Simulation results verify the effectiveness of the method compared with the classical OMP algorithm. The proposed method has higher estimation accuracy under the same noise level and observation number and is less affected by the scattering center spacing.