Neural Information Processing Systems http://nips.cc/

Biased gradient compression with error feedback (EF) reduces communication in federated learning (FL), but under non-IID data, the residual error can decay slowly, causing gradient mismatch and stalled progress in the early rounds. We propose step-ahead partial error feedback (SA-PEF), which integrates step-ahead (SA) correction with partial error feedback (PEF). SA-PEF recovers EF when the step-ahead coefficient α = 0 and step-ahead EF (SAEF) when α = 1. For non-convex objectives and δ-contractive compressors, we establish a second-moment bound and a residual recursion that guarantee convergence to stationar-ity under heterogeneous data and partial client participation. To balance SAEF's rapid warm-up with EF's long-term stability, we select α near its theory-predicted optimum. Experiments across diverse architectures and datasets show that SA-PEF consistently reaches target accuracy faster than EF. Modern large-scale machine learning increasingly relies on distributed computation, where both data and compute are spread across many devices. Federated learning (FL) enables model training in this setting without centralizing raw data, enhancing privacy and scalability under heterogeneous client distributions (McMahan et al., 2017; Kairouz et al., 2021). In each synchronous FL round, the server broadcasts the current global model to a subset of clients. These clients perform several steps of stochastic gradient descent (SGD) on their local data and return updates to the server, which aggregates them to form the next global iterate (Huang et al., 2022; Wang & Ji, 2022; Li et al., 2024). Although FL leverages rich distributed data, it faces two key challenges.

Due to the high communication overhead when training machine learning models in a distributed environment, modern algorithms invariably rely on lossy communication compression. However, when untreated, the errors caused by compression propagate, and can lead to severely unstable behavior, including exponential divergence. Almost a decade ago, Seide et al. [2014] proposed an error feedback (EF) mechanism, which we refer to as EF14, as an immensely effective heuristic for mitigating this issue. However, despite steady algorithmic and theoretical advances in the EF field in the last decade, our understanding is far from complete. In this work we address one of the most pressing issues.

The ensemble method is a promising way to mitigate the overestimation issue in Q-learning, where multiple function approximators are used to estimate the action values. It is known that the estimation bias hinges heavily on the ensemble size (i.e., the number of Q-function approximators used in the target), and that determining the'right' ensemble size is highly nontrivial, because of the time-varying nature of the function approximation errors during the learning process. To tackle this challenge, we first derive an upper bound and a lower bound on the estimation bias, based on which the ensemble size is adapted to drive the bias to be nearly zero, thereby coping with the impact of the time-varying approximation errors accordingly. Motivated by the theoretic findings, we advocate that the ensemble method can be combined with Model Identification Adaptive Control (MIAC) for effective ensemble size adaptation. Specifically, we devise Adaptive Ensemble Q-learning (AdaEQ), a generalized ensemble method with two key steps: (a) approximation error characterization which serves as the feedback for flexibly controlling the ensemble size, and (b) ensemble size adaptation tailored towards minimizing the estimation bias. Extensive experiments are carried out to show that AdaEQ can improve the learning performance than the existing methods for the MuJoCo benchmark.

In this paper, we propose a unified analysis of variants of distributed SGD with arbitrary compressions and delayed updates. Our framework is general enough to cover different variants of quantized SGD, Error-Compensated SGD (EC-SGD), and SGD with delayed updates (D-SGD). Via single theorem, we derive the complexity results for all the methods that fit our framework. For the existing methods, this theorem gives the best-known complexity results. Moreover, using our general scheme, we develop new variants of SGD that combine variance reduction or arbitrary sampling with error feedback and quantization and derive the convergence rates for these methods beating the state-of-the-art results. In order to illustrate the strength of our framework, we develop 16 new methods that fit this. In particular, we propose the first method called EC-SGD-DIANA that is based on error-feedback for biased compression operator and quantization of gradient differences and prove the convergence guarantees showing that EC-SGD-DIANA converges to the exact optimum asymptotically in expectation with constant learning rate for both convex and strongly convex objectives when workers compute full gradients of their loss functions. Moreover, for the case when the loss function of the worker has the form of finite sum, we modified the method and got a new one called EC-LSVRG-DIANA which is the first distributed stochastic method with error feedback and variance reduction that converges to the exact optimum asymptotically in expectation with constant learning rate.

Satellite constellations in low-Earth orbit are now widespread, enabling positioning, Earth imaging, and communications. In this paper we address the solution of learning problems using these satellite constellations. In particular, we focus on a federated approach, where satellites collect and locally process data, with the ground station aggregating local models. We focus on designing a novel, communication-efficient algorithm that still yields accurate trained models. To this end, we employ several mechanisms to reduce the number of communications with the ground station (local training) and their size (compression). We then propose an error feedback mechanism that enhances accuracy, which yields, as a byproduct, an algorithm-agnostic error feedback scheme that can be more broadly applied. We analyze the convergence of the resulting algorithm, and compare it with the state of the art through simulations in a realistic space scenario, showcasing superior performance.

Communication-efficient distributed training algorithms have received considerable interest recently due to their benefits for training Large Language Models (LLMs) in bandwidth-constrained settings, such as across datacenters and over the internet. Despite reducing communication frequency, these methods still typically require communicating a full copy of the model's gradients-resulting in a communication bottleneck even for cross-datacenter links. Furthermore, they can slightly degrade performance compared to a naive AdamW DDP baseline. While quantization is often applied to reduce the pseudo-gradient's size, in the context of LLM pre-training, existing approaches have been unable to additionally leverage sparsification and have obtained limited quantization. In this work, we introduce SparseLoCo, a communication-efficient training algorithm for LLMs that effectively leverages error feedback with Top-k sparsification and 2-bit quantization to reach extreme sparsity as low as 1-3% while outperforming full-precision DiLoCo. Our key observations are that outer momentum can be locally approximated by an error feedback accumulator combined with aggressive sparsity, and that sparse aggregation can actually improve model performance. We empirically demonstrate in a range of communication-constrained LLM training settings that SparseLoCo provides significant benefits in both performance and communication cost.

Abstract--Distributed optimization is pivotal for large-scale signal processing and machine learning, yet communication overhead remains a major bottleneck. Low-rank gradient compression, in which the transmitted gradients are approximated by low-rank matrices to reduce communication, offers a promising remedy. Existing methods typically adopt either randomized or greedy compression strategies: randomized approaches project gradients onto randomly chosen subspaces, introducing high variance and degrading empirical performance; greedy methods select the most informative subspaces, achieving strong empirical results but lacking convergence guarantees. T o address this gap, we propose GreedyLore--the first Greedy L ow-R ank gradie nt compression algorithm for distributed learning with rigorous convergence guarantees. GreedyLore incorporates error feedback to correct the bias introduced by greedy compression and introduces a semi-lazy subspace update that ensures the compression operator remains contractive throughout all iterations. With these techniques, we prove that GreedyLore achieves a convergence rate of O(σ/ NT+1/T) under standard optimizers such as MSGD and Adam--marking the first linear speedup convergence rate for low-rank gradient compression. Extensive experiments are conducted to validate our theoretical findings. Index T erms--Distributed Learning, Low-Rank Compression, Communication-Efficient Optimization, Error Feedback. ISTRIBUTED optimization is a promising paradigm for addressing large-scale problems in signal processing and machine learning. In distributed algorithms, each computing node processes its local data while collaborating with others to minimize a global loss function. This approach mitigates the computational burden on individual nodes, reduces memory requirements, and enables efficient parallel computation.

Objective: Robot-assisted minimally invasive surgery (RMIS) has become the gold standard for a variety of surgical procedures, but the optimal method of training surgeons for RMIS is unknown. We hypothesized that real-time, rather than post-task, error feedback would better increase learning speed and reduce errors. Methods: Forty-two surgical novices learned a virtual version of the ring-on-wire task, a canonical task in RMIS training. We investigated the impact of feedback timing with multi-sensory (haptic and visual) cues in three groups: (1) real-time error feedback, (2) trial replay with error feedback, and (3) no error feedback. Results: Participant performance was evaluated based on the accuracy of ring position and orientation during the task. Participants who received real-time feedback outperformed other groups in ring orientation. Additionally, participants who received feedback in replay outperformed participants who did not receive any error feedback on ring orientation during long, straight path sections. There were no significant differences between groups for ring position overall, but participants who received real-time feedback outperformed the other groups in positional accuracy on tightly curved path sections. Conclusion: The addition of real-time haptic and visual error feedback improves learning outcomes in a virtual surgical task over error feedback in replay or no error feedback at all. Significance: This work demonstrates that multi-sensory error feedback delivered in real time leads to better training outcomes as compared to the same feedback delivered after task completion. This novel method of training may enable surgical trainees to develop skills with greater speed and accuracy.