In off-policy policy evaluation (OPE) tasks within reinforcement learning, Temporal Difference Learning(TD) and Fitted Q-Iteration (FQI) have traditionally been viewed as differing in the number of updates toward the target value function: TD makes one update, FQI makes an infinite number, and Partial Fitted Q-Iteration (PFQI) performs a finite number. We show that this view is not accurate, and provide a new mathematical perspective under linear value function approximation that unifies these methods as a single iterative method solving same linear system, but using different matrix splitting schemes and preconditioners. We show that increasing the number of updates under the same target value function, i.e., the target network technique, is a transition from using a constant preconditioner to using a data-feature adaptive preconditioner. This elucidates, for the first time, why TD convergence does not necessarily imply FQI convergence, and establishes tight convergence connections among TD, PFQI, and FQI. Our framework enables sharper theoretical results than previous work and characterization of the convergence conditions for each algorithm, without relying on assumptions about the features (e.g., linear independence). We also provide an encoder-decoder perspective to better understand TD's convergence conditions, and prove, for the first time, that when a large learning rate doesn't work, trying a smaller one may help(for batch TD). Our framework also leads to the discovery of new crucial conditions on features for convergence, and shows how common assumptions about features influence convergence, e.g., the assumption of linearly independent features can be dropped without compromising the convergence guarantees of stochastic TD in the on-policy setting. This paper is also the first to introduce matrix splitting into the convergence analysis of these algorithms.

We propose ACProp (Asynchronous-centering-Prop), an adaptive optimizer which combines centering of second momentum and asynchronous update (e.g. for $t$-th update, denominator uses information up to step $t-1$, while numerator uses gradient at $t$-th step). ACProp has both strong theoretical properties and empirical performance. With the example by Reddi et al. (2018), we show that asynchronous optimizers (e.g. AdaShift, ACProp) have weaker convergence condition than synchronous optimizers (e.g. Adam, RMSProp, AdaBelief); within asynchronous optimizers, we show that centering of second momentum further weakens the convergence condition. We demonstrate that ACProp has a convergence rate of $O(\frac{1}{\sqrt{T}})$ for the stochastic non-convex case, which matches the oracle rate and outperforms the $O(\frac{logT}{\sqrt{T}})$ rate of RMSProp and Adam. We validate ACProp in extensive empirical studies: ACProp outperforms both SGD and other adaptive optimizers in image classification with CNN, and outperforms well-tuned adaptive optimizers in the training of various GAN models, reinforcement learning and transformers. To sum up, ACProp has good theoretical properties including weak convergence condition and optimal convergence rate, and strong empirical performance including good generalization like SGD and training stability like Adam.

Federated Learning (FL) enables collaborative model training across decentralized data sources while preserving data privacy. However, the growing size of Machine Learning (ML) models poses communication and computation challenges in FL. Low-Rank Adaptation (LoRA) has recently been introduced into FL as an efficient fine-tuning method, reducing communication overhead by updating only a small number of trainable parameters. Despite its effectiveness, how to aggregate LoRA-updated local models on the server remains a critical and understudied problem. In this paper, we provide a unified convergence analysis for LoRA-based FL. We first categories the current aggregation method into two major type: Sum-Product (SP) and Product-Sum (PS). Then we formally define the Aggregation-Broadcast Operator (ABO) and derive both weak and strong convergence condition under mild assumptions. Furthermore, we present both weak and strong convergence condition that guarantee convergence of the local model and the global model respectively. These theoretical analyze offer a principled understanding of various aggregation strategies. Notably, we prove that the SP and PS aggregation methods satisfy the weak and strong convergence condition respectively, but differ in their ability to achieve the optimal convergence rate. Extensive experiments on standard benchmarks validate our theoretical findings.

We introduce a frequency-domain framework for convergence analysis of hyperparameters in game optimization, leveraging High-Resolution Differential Equations (HRDEs) and Laplace transforms. Focusing on the Lookahead algorithm--characterized by gradient steps $k$ and averaging coefficient $α$--we transform the discrete-time oscillatory dynamics of bilinear games into the frequency domain to derive precise convergence criteria. Our higher-precision $O(γ^2)$-HRDE models yield tighter criteria, while our first-order $O(γ)$-HRDE models offer practical guidance by prioritizing actionable hyperparameter tuning over complex closed-form solutions. Empirical validation in discrete-time settings demonstrates the effectiveness of our approach, which may further extend to locally linear operators, offering a scalable framework for selecting hyperparameters for learning in games.

In recent years, Vision-Language-Action (VLA) models have become a vital research direction in robotics due to their impressive multimodal understanding and generalization capabilities. Despite the progress, their practical deployment is severely constrained by inference speed bottlenecks, particularly in high-frequency and dexterous manipulation tasks. While recent studies have explored Jacobi decoding as a more efficient alternative to traditional autoregressive decoding, its practical benefits are marginal due to the lengthy iterations. To address it, we introduce consistency distillation training to predict multiple correct action tokens in each iteration, thereby achieving acceleration. Besides, we design mixed-label supervision to mitigate the error accumulation during distillation. Although distillation brings acceptable speedup, we identify that certain inefficient iterations remain a critical bottleneck. To tackle this, we propose an early-exit decoding strategy that moderately relaxes convergence conditions, which further improves average inference efficiency. Experimental results show that the proposed method achieves more than 4 times inference acceleration across different baselines while maintaining high task success rates in both simulated and real-world robot tasks. These experiments validate that our approach provides an efficient and general paradigm for accelerating multimodal decision-making in robotics. Our project page is available at https://irpn-eai.github.io/CEED-VLA/.

We propose ACProp (Asynchronous-centering-Prop), an adaptive optimizer which combines centering of second momentum and asynchronous update (e.g. for t -th update, denominator uses information up to step t-1, while numerator uses gradient at t -th step). ACProp has both strong theoretical properties and empirical performance. With the example by Reddi et al. (2018), we show that asynchronous optimizers (e.g. AdaShift, ACProp) have weaker convergence condition than synchronous optimizers (e.g. Adam, RMSProp, AdaBelief); within asynchronous optimizers, we show that centering of second momentum further weakens the convergence condition.

We propose a new learning method, "Generalized Learning Vec(cid:173) tor Quantization (GLVQ)," in which reference vectors are updated based on the steepest descent method in order to minimize the cost function . The cost function is determined so that the obtained learning rule satisfies the convergence condition. We prove that Kohonen's rule as used in LVQ does not satisfy the convergence condition and thus degrades recognition ability. Experimental re(cid:173) sults for printed Chinese character recognition reveal that GLVQ is superior to LVQ in recognition ability.

In this paper, we propose a novel primal-dual proximal splitting algorithm (PD-PSA), named BALPA, for the composite optimization problem with equality constraints, where the loss function consists of a smooth term and a nonsmooth term composed with a linear mapping. In BALPA, the dual update is designed as a proximal point for a time-varying quadratic function, which balances the implementation of primal and dual update and retains the proximity-induced feature of classic PD-PSAs. In addition, by this balance, BALPA eliminates the inefficiency of classic PD-PSAs for composite optimization problems in which the Euclidean norm of the linear mapping or the equality constraint mapping is large. Therefore, BALPA not only inherits the advantages of simple structure and easy implementation of classic PD-PSAs but also ensures a fast convergence when these norms are large. Moreover, we propose a stochastic version of BALPA (S-BALPA) and apply the developed BALPA to distributed optimization to devise a new distributed optimization algorithm. Furthermore, a comprehensive convergence analysis for BALPA and S-BALPA is conducted, respectively. Finally, numerical experiments demonstrate the efficiency of the proposed algorithms.