arXiv subjects

Konstantin Mishchenko

Publications and source records attributed to Konstantin Mishchenko.

At least 19 recordsLinked to original sources

arXiv2025

Smoothing DiLoCo with Primal Averaging for Faster Training of LLMs

We propose Generalized Primal Averaging (GPA), an extension of Nesterov's method that unifies and generalizes recent averaging-based optimizers like single-worker DiLoCo and Schedule-Free, within a non-distributed setting. While DiLoCo relies on a memory-intensive two-loop structure to periodically aggregate pseudo-gradients using Nesterov momentum, GPA eliminates this complexity by decoupling Nesterov's interpolation constants to enable smooth iterate averaging at every step. Structurally, GPA resembles Schedule-Free but replaces uniform averaging with exponential moving averaging. Empirically, GPA consistently outperforms single-worker DiLoCo and AdamW with reduced memory overhead. GPA achieves speedups of 8.71%, 10.13%, and 9.58% over the AdamW baseline in terms of steps to reach target validation loss for Llama-160M, 1B, and 8B models, respectively. Similarly, on the ImageNet ViT workload, GPA achieves speedups of 7% and 25.5% in the small and large batch settings respectively. Furthermore, we prove that for any base optimizer with $O(\sqrt{T})$ regret, where $T$ is the number of iterations, GPA matches or exceeds the original convergence guarantees depending on the interpolation constants.

cs.LG↗

arXiv2025

Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillation

We provide a general convergence theorem of an idealized stochastic Polyak step size called SPS$^*$. Besides convexity, we only assume a local expected gradient bound, that includes locally smooth and locally Lipschitz losses as special cases. We refer to SPS$^*$ as idealized because it requires access to the loss for every training batch evaluated at a solution. It is also ideal, in that it achieves the optimal lower bound for globally Lipschitz function, and is the first Polyak step size to have an $O(1/\sqrt{t})$ anytime convergence in the smooth setting. We show how to combine SPS$^*$ with momentum to achieve the same favorable rates for the last iterate. We conclude with several experiments to validate our theory, and a more practical setting showing how we can distill a teacher GPT-2 model into a smaller student model without any hyperparameter tuning.

cs.LG↗

arXiv2024

Hardware-Aware Parallel Prompt Decoding for Memory-Efficient Acceleration of LLM Inference

The auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance. While recent research has investigated various speculative decoding techniques for multi-token generation, these efforts have primarily focused on improving processing speed such as throughput. Crucially, they often neglect other metrics essential for real-life deployments, such as memory consumption and training cost. To overcome these limitations, we propose a novel parallel prompt decoding that requires only $0.0002$% trainable parameters, enabling efficient training on a single A100-40GB GPU in just 16 hours. Inspired by the human natural language generation process, $PPD$ approximates outputs generated at future timesteps in parallel by using multiple prompt tokens. This approach partially recovers the missing conditional dependency information necessary for multi-token generation, resulting in up to a 28% higher acceptance rate for long-range predictions. Furthermore, we present a hardware-aware dynamic sparse tree technique that adaptively optimizes this decoding scheme to fully leverage the computational capacities on different GPUs. Through extensive experiments across LLMs ranging from MobileLlama to Vicuna-13B on a wide range of benchmarks, our approach demonstrates up to 2.49$\times$ speedup and maintains a minimal runtime memory overhead of just $0.0004$%. More importantly, our parallel prompt decoding can serve as an orthogonal optimization for synergistic integration with existing speculative decoding, showing up to $1.22\times$ further speed improvement. Our code is available at https://github.com/hmarkc/parallel-prompt-decoding.

cs.LG↗

arXiv2024

The Road Less Scheduled

Existing learning rate schedules that do not require specification of the optimization stopping step T are greatly out-performed by learning rate schedules that depend on T. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhibiting state-of-the-art performance compared to schedules across a wide family of problems ranging from convex problems to large-scale deep learning problems. Our Schedule-Free approach introduces no additional hyper-parameters over standard optimizers with momentum. Our method is a direct consequence of a new theory we develop that unifies scheduling and iterate averaging. An open source implementation of our method is available at https://github.com/facebookresearch/schedule_free. Schedule-Free AdamW is the core algorithm behind our winning entry to the MLCommons 2024 AlgoPerf Algorithmic Efficiency Challenge Self-Tuning track.

cs.LG↗

arXiv2024

Prodigy: An Expeditiously Adaptive Parameter-Free Learner

We consider the problem of estimating the learning rate in adaptive methods, such as AdaGrad and Adam. We propose Prodigy, an algorithm that provably estimates the distance to the solution $D$, which is needed to set the learning rate optimally. At its core, Prodigy is a modification of the D-Adaptation method for learning-rate-free learning. It improves upon the convergence rate of D-Adaptation by a factor of $O(\sqrt{\log(D/d_0)})$, where $d_0$ is the initial estimate of $D$. We test Prodigy on 12 common logistic-regression benchmark datasets, VGG11 and ResNet-50 training on CIFAR10, ViT training on Imagenet, LSTM training on IWSLT14, DLRM training on Criteo dataset, VarNet on Knee MRI dataset, as well as RoBERTa and GPT transformer training on BookWiki. Our experimental results show that our approach consistently outperforms D-Adaptation and reaches test accuracy values close to that of hand-tuned Adam.

cs.LG↗

arXiv2024

Adaptive Proximal Gradient Method for Convex Optimization

In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions. We propose adaptive versions of GD and ProxGD that are based on observed gradient differences and, thus, have no added computational costs. Moreover, we prove convergence of our methods assuming only local Lipschitzness of the gradient. In addition, the proposed versions allow for even larger stepsizes than those initially suggested in [MM20].

math.OC↗

arXiv2024

DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Method

This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient -- matching the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor without tuning any parameters, and universal -- automatically adapting to both smooth and nonsmooth problems. While popular algorithms following the AdaGrad framework compute a running average of the squared gradients to use for normalization, DoWG maintains a new distance-based weighted version of the running average, which is crucial to achieve the desired properties. To complement our theory, we also show empirically that DoWG trains at the edge of stability, and validate its effectiveness on practical machine learning tasks.

cs.LG↗

arXiv2023

Distributed Learning with Compressed Gradient Differences

Training large machine learning models requires a distributed computing approach, with communication of the model updates being the bottleneck. For this reason, several methods based on the compression (e.g., sparsification and/or quantization) of updates were recently proposed, including QSGD (Alistarh et al., 2017), TernGrad (Wen et al., 2017), SignSGD (Bernstein et al., 2018), and DQGD (Khirirat et al., 2018). However, none of these methods are able to learn the gradients, which renders them incapable of converging to the true optimum in the batch mode. In this work we propose a new distributed learning method -- DIANA -- which resolves this issue via compression of gradient differences. We perform a theoretical analysis in the strongly convex and nonconvex settings and show that our rates are superior to existing rates. We also provide theory to support non-smooth regularizers study the difference between quantization schemes. Our analysis of block-quantization and differences between $\ell_2$ and $\ell_{\infty}$ quantization closes the gaps in theory and practice. Finally, by applying our analysis technique to TernGrad, we establish the first convergence rate for this method.

cs.LG↗

arXiv2023

Optimal Linear Decay Learning Rate Schedules and Further Refinements

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our main technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). When considering only worst-case analysis, our theory predicts that the optimal choice is the linear decay schedule where the step-size is set proportional to 1 - t/T, where t is the current iteration and T is the total number of steps. To go beyond this worst-case analysis, we use the observed gradient norms to derive schedules refined for any particular task. These refined schedules exhibit learning rate warm-up and rapid learning rate annealing near the end of training. Ours is the first systematic approach to automatically yield both of these properties. We perform the most comprehensive evaluation of learning rate schedules to date, evaluating across 10 diverse deep learning problems, a series of LLMs, and a suite of logistic regression problems. We validate that overall, the linear-decay schedule outperforms all commonly used default schedules including cosine annealing. Our adaptive schedule refinement method gives further improvements.

cs.LG↗

arXiv2023

Learning-Rate-Free Learning by D-Adaptation

D-Adaptation is an approach to automatically setting the learning rate which asymptotically achieves the optimal rate of convergence for minimizing convex Lipschitz functions, with no back-tracking or line searches, and no additional function value or gradient evaluations per step. Our approach is the first hyper-parameter free method for this class without additional multiplicative log factors in the convergence rate. We present extensive experiments for SGD and Adam variants of our method, where the method automatically matches hand-tuned learning rates across more than a dozen diverse machine learning problems, including large-scale vision and language problems. An open-source implementation is available.

cs.LG↗

arXiv2023

Two Losses Are Better Than One: Faster Optimization Using a Cheaper Proxy

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is $δ$-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a $δ$-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

cs.LG↗

arXiv2023

Partially Personalized Federated Learning: Breaking the Curse of Data Heterogeneity

We present a partially personalized formulation of Federated Learning (FL) that strikes a balance between the flexibility of personalization and cooperativeness of global training. In our framework, we split the variables into global parameters, which are shared across all clients, and individual local parameters, which are kept private. We prove that under the right split of parameters, it is possible to find global parameters that allow each client to fit their data perfectly, and refer to the obtained problem as overpersonalized. For instance, the shared global parameters can be used to learn good data representations, whereas the personalized layers are fine-tuned for a specific client. Moreover, we present a simple algorithm for the partially personalized formulation that offers significant benefits to all clients. In particular, it breaks the curse of data heterogeneity in several settings, such as training with local steps, asynchronous training, and Byzantine-robust training.

cs.LG↗

arXiv2023

Asynchronous SGD Beats Minibatch SGD Under Arbitrary Delays

The existing analysis of asynchronous stochastic gradient descent (SGD) degrades dramatically when any delay is large, giving the impression that performance depends primarily on the delay. On the contrary, we prove much better guarantees for the same asynchronous SGD algorithm regardless of the delays in the gradients, depending instead just on the number of parallel devices used to implement the algorithm. Our guarantees are strictly better than the existing analyses, and we also argue that asynchronous SGD outperforms synchronous minibatch SGD in the settings we consider. For our analysis, we introduce a novel recursion based on "virtual iterates" and delay-adaptive stepsizes, which allow us to derive state-of-the-art guarantees for both convex and non-convex objectives.

math.OC↗

arXiv2023

ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!

We introduce ProxSkip -- a surprisingly simple and provably efficient method for minimizing the sum of a smooth ($f$) and an expensive nonsmooth proximable ($ψ$) function. The canonical approach to solving such problems is via the proximal gradient descent (ProxGD) algorithm, which is based on the evaluation of the gradient of $f$ and the prox operator of $ψ$ in each iteration. In this work we are specifically interested in the regime in which the evaluation of prox is costly relative to the evaluation of the gradient, which is the case in many applications. ProxSkip allows for the expensive prox operator to be skipped in most iterations: while its iteration complexity is $\mathcal{O}\left(κ\log \frac{1}{\varepsilon}\right)$, where $κ$ is the condition number of $f$, the number of prox evaluations is $\mathcal{O}\left(\sqrtκ \log \frac{1}{\varepsilon}\right)$ only. Our main motivation comes from federated learning, where evaluation of the gradient operator corresponds to taking a local GD step independently on all devices, and evaluation of prox corresponds to (expensive) communication in the form of gradient averaging. In this context, ProxSkip offers an effective acceleration of communication complexity. Unlike other local gradient-type methods, such as FedAvg, SCAFFOLD, S-Local-GD and FedLin, whose theoretical communication complexity is worse than, or at best matching, that of vanilla GD in the heterogeneous data regime, we obtain a provable and large improvement without any heterogeneity-bounding assumptions.

cs.LG↗

arXiv2023

Regularized Newton Method with Global $O(1/k^2)$ Convergence

We present a Newton-type method that converges fast from any initialization and for arbitrary convex objectives with Lipschitz Hessians. We achieve this by merging the ideas of cubic regularization with a certain adaptive Levenberg--Marquardt penalty. In particular, we show that the iterates given by $x^{k+1}=x^k - \bigl(\nabla^2 f(x^k) + \sqrt{H\|\nabla f(x^k)\|} \mathbf{I}\bigr)^{-1}\nabla f(x^k)$, where $H>0$ is a constant, converge globally with a $\mathcal{O}(\frac{1}{k^2})$ rate. Our method is the first variant of Newton's method that has both cheap iterations and provably fast global convergence. Moreover, we prove that locally our method converges superlinearly when the objective is strongly convex. To boost the method's performance, we present a line search procedure that does not need prior knowledge of $H$ and is provably efficient.

math.OC↗

arXiv2023

Convergence of First-Order Algorithms for Meta-Learning with Moreau Envelopes

In this work, we consider the problem of minimizing the sum of Moreau envelopes of given functions, which has previously appeared in the context of meta-learning and personalized federated learning. In contrast to the existing theory that requires running subsolvers until a certain precision is reached, we only assume that a finite number of gradient steps is taken at each iteration. As a special case, our theory allows us to show the convergence of First-Order Model-Agnostic Meta-Learning (FO-MAML) to the vicinity of a solution of Moreau objective. We also study a more general family of first-order algorithms that can be viewed as a generalization of FO-MAML. Our main theoretical achievement is a theoretical improvement upon the inexact SGD framework. In particular, our perturbed-iterate analysis allows for tighter guarantees that improve the dependency on the problem's conditioning. In contrast to the related work on meta-learning, ours does not require any assumptions on the Hessian smoothness, and can leverage smoothness and convexity of the reformulation based on Moreau envelopes. Furthermore, to fill the gaps in the comparison of FO-MAML to the Implicit MAML (iMAML), we show that the objective of iMAML is neither smooth nor convex, implying that it has no convergence guarantees based on the existing theory.

math.OC↗

arXiv2022

Super-Universal Regularized Newton Method

We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the gradient norm at the current point. We introduce a family of problem classes characterized by Hölder continuity of either the second or third derivative. Then we present the method with a simple adaptive search procedure allowing an automatic adjustment to the problem class with the best global complexity bounds, without knowing specific parameters of the problem. In particular, for the class of functions with Lipschitz continuous third derivative, we get the global $O(1/k^3)$ rate, which was previously attributed to third-order tensor methods. When the objective function is uniformly convex, we justify an automatic acceleration of our scheme, resulting in a faster global rate and local superlinear convergence. The switching between the different rates (sublinear, linear, and superlinear) is automatic. Again, for that, no a priori knowledge of parameters is needed.

math.OC↗

arXiv2022

Adaptive Learning Rates for Faster Stochastic Gradient Methods

In this work, we propose new adaptive step size strategies that improve several stochastic gradient methods. Our first method (StoPS) is based on the classical Polyak step size (Polyak, 1987) and is an extension of the recent development of this method for the stochastic optimization-SPS (Loizou et al., 2021), and our second method, denoted GraDS, rescales step size by "diversity of stochastic gradients". We provide a theoretical analysis of these methods for strongly convex smooth functions and show they enjoy deterministic-like rates despite stochastic gradients. Furthermore, we demonstrate the theoretical superiority of our adaptive methods on quadratic objectives. Unfortunately, both StoPS and GraDS depend on unknown quantities, which are only practical for the overparametrized models. To remedy this, we drop this undesired dependence and redefine StoPS and GraDS to StoP and GraD, respectively. We show that these new methods converge linearly to the neighbourhood of the optimal solution under the same assumptions. Finally, we corroborate our theoretical claims by experimental validation, which reveals that GraD is particularly useful for deep learning optimization.

cs.LG↗