Convergence Analysis of the Lion Optimizer in Centralized and Distributed Settings

In this paper, we analyze the convergence properties of the Lion optimizer. First, we establish that the Lion optimizer attains a convergence rate of $\mathcal{O}(d^{1/2}T^{-1/4})$ under standard assumptions, where $d$ denotes the problem dimension and $T$ is the iteration number. To further improve this rate, we introduce the Lion optimizer with variance reduction, resulting in an enhanced convergence rate of $\mathcal{O}(d^{1/2}T^{-1/3})$. We then analyze in distributed settings, where the standard and variance reduced version of the distributed Lion can obtain the convergence rates of $\mathcal{O}(d^{1/2}(nT)^{-1/4})$ and $\mathcal{O}(d^{1/2}(nT)^{-1/3})$, with $n$ denoting the number of nodes. Furthermore, we investigate a communication-efficient variant of the distributed Lion that ensures sign compression in both communication directions. By employing the unbiased sign operations, the proposed Lion variant and its variance reduction counterpart, achieve convergence rates of $\mathcal{O}\left( \max \left\{\frac{d^{1/4}}{T^{1/4}}, \frac{d^{1/10}}{n^{1/5}T^{1/5}} \right\} \right)$ and $\mathcal{O}\left( \frac{d^{1/4}}{T^{1/4}} \right)$, respectively.

Improved Analysis for Sign-based Methods with Momentum Updates

In this paper, we present enhanced analysis for sign-based optimization algorithms with momentum updates. Traditional sign-based methods, under the separable smoothness assumption, guarantee a convergence rate of $\mathcal{O}(T^{-1/4})$, but they either require large batch sizes or assume unimodal symmetric stochastic noise. To address these limitations, we demonstrate that signSGD with momentum can achieve the same convergence rate using constant batch sizes without additional assumptions. Our analysis, under the standard $l_2$-smoothness condition, improves upon the result of the prior momentum-based signSGD method by a factor of $\mathcal{O}(d^{1/2})$, where $d$ is the problem dimension. Furthermore, we explore sign-based methods with majority vote in distributed settings and show that the proposed momentum-based method yields convergence rates of $\mathcal{O}\left( d^{1/2}T^{-1/2} + dn^{-1/2} \right)$ and $\mathcal{O}\left( \max \{ d^{1/4}T^{-1/4}, d^{1/10}T^{-1/5} \} \right)$, which outperform the previous results of $\mathcal{O}\left( dT^{-1/4} + dn^{-1/2} \right)$ and $\mathcal{O}\left( d^{3/8}T^{-1/8} \right)$, respectively. Numerical experiments further validate the effectiveness of the proposed methods.

Topology Enhanced MARL for Multi-Vehicle Cooperative Decision-Making of CAVs

The exploration-exploitation trade-off constitutes one of the fundamental challenges in reinforcement learning (RL), which is exacerbated in multi-agent reinforcement learning (MARL) due to the exponential growth of joint state-action spaces. This paper proposes a topology-enhanced MARL (TPE-MARL) method for optimizing cooperative decision-making of connected and autonomous vehicles (CAVs) in mixed traffic. This work presents two primary contributions: First, we construct a game topology tensor for dynamic traffic flow, effectively compressing high-dimensional traffic state information and decrease the search space for MARL algorithms. Second, building upon the designed game topology tensor and using QMIX as the backbone RL algorithm, we establish a topology-enhanced MARL framework incorporating visit counts and agent mutual information. Extensive simulations across varying traffic densities and CAV penetration rates demonstrate the effectiveness of TPE-MARL. Evaluations encompassing training dynamics, exploration patterns, macroscopic traffic performance metrics, and microscopic vehicle behaviors reveal that TPE-MARL successfully balances exploration and exploitation. Consequently, it exhibits superior performance in terms of traffic efficiency, safety, decision smoothness, and task completion. Furthermore, the algorithm demonstrates decision-making rationality comparable to or exceeding that of human drivers in both mixed-autonomy and fully autonomous traffic scenarios. Code of our work is available at \href{https://github.com/leoPub/tpemarl}{https://github.com/leoPub/tpemarl}.

Risk-aware Direct Preference Optimization under Nested Risk Measure

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

Discounted Online Convex Optimization: Uniform Regret Across a Continuous Interval

Reflecting the greater significance of recent history over the distant past in non-stationary environments, $\lambda$-discounted regret has been introduced in online convex optimization (OCO) to gracefully forget past data as new information arrives. When the discount factor $\lambda$ is given, online gradient descent with an appropriate step size achieves an $O(1/\sqrt{1-\lambda})$ discounted regret. However, the value of $\lambda$ is often not predetermined in real-world scenarios. This gives rise to a significant open question: is it possible to develop a discounted algorithm that adapts to an unknown discount factor. In this paper, we affirmatively answer this question by providing a novel analysis to demonstrate that smoothed OGD (SOGD) achieves a uniform $O(\sqrt{\log T/1-\lambda})$ discounted regret, holding for all values of $\lambda$ across a continuous interval simultaneously. The basic idea is to maintain multiple OGD instances to handle different discount factors, and aggregate their outputs sequentially by an online prediction algorithm named as Discounted-Normal-Predictor (DNP) (Kapralov and Panigrahy,2010). Our analysis reveals that DNP can combine the decisions of two experts, even when they operate on discounted regret with different discount factors.

Communication-Efficient Multi-Device Inference Acceleration for Transformer Models

Transformer models power many AI applications but suffer from high inference latency, limiting their use in real-time settings. Multi-device inference can reduce latency by parallelizing computation. Yet, existing methods require high inter-device bandwidth, making them impractical for bandwidth-constrained environments. We propose ASTRA, a communication-efficient framework that accelerates Transformer inference through a novel integration of sequence parallelism and a Mixed-Precision Attention mechanism designed to minimize inter-device communication. ASTRA compresses non-local token embeddings via vector quantization and preserves task accuracy through two optimizations, Noise-Augmented Quantization and Distributed Class Tokens. Experiments on ViT and GPT2 across vision and NLP tasks show that ASTRA achieves up to 2.64X speedups over single-device inference and up to 15.25X speedups over state-of-the-art multi-device inferences, while operating under bandwidths as low as 10 Mbps. ASTRA is open-sourced at https://github.com/xl1990/Astra.

Continuous Subspace Optimization for Continual Learning

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when acquiring new knowledge. Recently, approaches leveraging pre-trained models have gained increasing popularity to mitigate this issue, due to the strong generalization ability of foundation models. To adjust pre-trained models for new tasks, existing methods usually employ low-rank adaptation, which restricts parameter updates to a fixed low-rank subspace. However, constraining the optimization space inherently compromises the model's learning capacity, resulting in inferior performance. To address the limitation, we propose Continuous Subspace Optimization for Continual Learning (CoSO) to fine-tune the model in a series of subspaces rather than a single one. These sequential subspaces are dynamically determined through the singular value decomposition of gradients. CoSO updates the model by projecting gradients into these subspaces, ensuring memory-efficient optimization. To mitigate forgetting, the optimization subspaces of each task are set to be orthogonal to the historical task subspace. During task learning, CoSO maintains a task-specific component that captures the critical update directions associated with the current task. Upon completing a task, this component is used to update the historical task subspace, laying the groundwork for subsequent learning. Extensive experiments on multiple datasets demonstrate that CoSO significantly outperforms state-of-the-art methods, especially in challenging scenarios with long task sequences.

External Knowledge Injection for CLIP-Based Class-Incremental Learning

Class-Incremental Learning (CIL) enables learning systems to continuously adapt to evolving data streams. With the advancement of pre-training, leveraging pre-trained vision-language models (e.g., CLIP) offers a promising starting point for CIL. However, CLIP makes decisions by matching visual embeddings to class names, overlooking the rich contextual information conveyed through language. For instance, the concept of ``cat'' can be decomposed into features like tail, fur, and face for recognition. Besides, since the model is continually updated, these detailed features are overwritten in CIL, requiring external knowledge for compensation. In this paper, we introduce ExterNal knowledGe INjEction (ENGINE) for CLIP-based CIL. To enhance knowledge transfer from outside the dataset, we propose a dual-branch injection tuning framework that encodes informative knowledge from both visual and textual modalities. The visual branch is enhanced with data augmentation to enrich the visual features, while the textual branch leverages GPT-4 to rewrite discriminative descriptors. In addition to this on-the-fly knowledge injection, we also implement post-tuning knowledge by re-ranking the prediction results during inference. With the injected knowledge, the model can better capture informative features for downstream tasks as data evolves. Extensive experiments demonstrate the state-of-the-art performance of ENGINE. Code is available at: https://github.com/RenaissCode/ENGINE

Generalizability of Neural Networks Minimizing Empirical Risk Based on Expressive Ability

The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep learning exhibit nice generalizability. On the other hand, algorithm-dependent generalization bounds, like stability bounds, often rely on strict assumptions. To establish generalizability under less stringent assumptions, this paper investigates the generalizability of neural networks that minimize or approximately minimize empirical risk. We establish a lower bound for population accuracy based on the expressiveness of these networks, which indicates that with an adequate large number of training samples and network sizes, these networks, including over-parameterized ones, can generalize effectively. Additionally, we provide a necessary condition for generalization, demonstrating that, for certain data distributions, the quantity of training data required to ensure generalization exceeds the network size needed to represent the corresponding data distribution. Finally, we provide theoretical insights into several phenomena in deep learning, including robust generalization, importance of over-parameterization, and effect of loss function on generalization.

PVBF: A Framework for Mitigating Parameter Variation Imbalance in Online Continual Learning

Online continual learning (OCL), which enables AI systems to adaptively learn from non-stationary data streams, is commonly achieved using experience replay (ER)-based methods that retain knowledge by replaying stored past during training. However, these methods face challenges of prediction bias, stemming from deviations in parameter update directions during task transitions. This paper identifies parameter variation imbalance as a critical factor contributing to prediction bias in ER-based OCL. Specifically, using the proposed parameter variation evaluation method, we highlight two types of imbalance: correlation-induced imbalance, where certain parameters are disproportionately updated across tasks, and layer-wise imbalance, where output layer parameters update faster than those in preceding layers. To mitigate the above imbalances, we propose the Parameter Variation Balancing Framework (PVBF), which incorporates: 1) a novel method to compute parameter correlations with previous tasks based on parameter variations, 2) an encourage-and-consolidate (E&C) method utilizing parameter correlations to perform gradient adjustments across all parameters during training, 3) a dual-layer copy weights with reinit (D-CWR) strategy to slowly update output layer parameters for frequently occuring sample categories. Experiments on short and long task sequences demonstrate that PVBF significantly reduces prediction bias and improves OCL performance, achieving up to 47\% higher accuracy compared to existing ER-based methods.