New algorithm Momentum-QNG improves optimization of quantum circuits.
problem Optimizing variational quantum circuits to avoid local minima.
method Applied Langevin dynamics to QNG, introducing momentum term.
result Momentum-QNG outperforms basic QNG and other optimizers.
Paper develops momentum schemes with variance reduction for non-convex composition optimization.
problem Lack of convergence guarantee and efficient momentum design in existing algorithms.
method Develops various momentum schemes with SPIDER-based variance reduction.
result Achieves near-optimal sample complexity and linear convergence rate.
New method uses momentum to converge in DC optimization with small batches.
problem Lack of convergence properties for stochastic difference-of-convex optimization with small batch sizes.
method Introduces momentum to enable convergence under standard assumptions for any batch size.
result Proves convergence of the algorithm under smoothness and bounded variance assumptions.
New method shows stochastic momentum can converge quickly on optimization problems.
problem Improving convergence of stochastic optimization methods.
method Stochastic heavy ball momentum with minibatching.
result Stochastic heavy ball momentum retains fast linear rate on quadratic problems.
Optimization algorithms with momentum, e.g., (ADAM), have been widely used for building deep learning models due to the faster convergence rates compared with stochastic gradient descent (SGD). Momentum helps accelerate SGD in the relevant directions in parameter updating, which can minify the oscillations of parameter…
The paper analyzes how hyperparameters affect SGD with momentum's convergence rate.
problem The role of hyperparameters in SGD with momentum's convergence rate.
method Theoretical analysis using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE).
result The optimal linear rate of convergence depends on both the learning rate and the momentum coefficient.
SMG combines shuffling and momentum for non-convex optimization.
problem Non-convex finite-sum optimization problems.
method Shuffling Gradient-based method with momentum.
result Established state-of-the-art convergence rates for SMG.
Negative momentum accelerates convergence in minimax games but at a suboptimal rate.
problem The convergence rate of negative momentum in minimax games is suboptimal.
method Extending variational inequality formulation, connecting momentum method with Chebyshev polynomials.
result Negative momentum accelerates convergence locally but at a suboptimal rate.
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
Adaptive momentum method solves non-convex min-max problems.
problem Non-convex min-max optimization problems in training generative adversarial networks.
method Proposes an adaptive momentum algorithm for non-convex min-max optimization.
result Establishes non-asymptotic convergence rates for the proposed algorithm.
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
A new principle for optimizer selection improves training speed and performance.
problem Finding the best optimizer hyperparameters for faster training.
method Formulate optimizer selection as maximizing the expected drop rate in loss, treating gradients and updates as signals and an optimizer as a causal filter.
result Greedy optimizer selection yields stable and effective momentum rules.
We adapt the optimization's concept of momentum to reinforcement learning. Seeing the state-action value functions as an analog to the gradients in optimization, we interpret momentum as an average of consecutive q-functions. We derive Momentum Value Iteration (MoVI), a variation of Value Iteration that incorporates …
The study analyzes momentum-based optimization algorithms from dynamical systems perspective.
problem Understanding convergence rates of momentum-based optimization algorithms.
method Exploits dynamical systems, control theory, and symplectic perspectives to analyze convergence rates.
result Provides closed-form expressions relating algorithm parameters to convergence rates.
Stochastic proximal point algorithm with momentum converges faster and is more stable than standard methods.
problem Improving convergence and stability of stochastic optimization methods.
method Developed and analyzed the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM).
result SPPAM converges faster and is more stable than standard stochastic proximal point algorithm (SPPA) and stochastic gradient descent with momentum (SGDM).
Improved convergence for Polyak steps with momentum in smooth convex optimization.
problem Optimizing smooth strongly convex functions with limited information.
method Polyak steps with momentum, derived for accelerated gradient method.
result Convergence guarantees for accelerated gradient method with Polyak steps and momentum.
This paper analyzes two Lie group momentum optimization algorithms and their convergence rates.
problem Optimizing functions on Lie groups using momentum-based dynamics.
method Investigates Lie Heavy-Ball and Lie NAG-SC algorithms, quantifying their convergence rates under smoothness and convexity assumptions.
result Lie NAG-SC accelerates optimization over the momentumless case, while Lie Heavy-Ball does not.
Momentum affects optimization differently at small vs large batch sizes near instability.
problem Understanding how momentum impacts optimization near the edge of stability.
method Demonstrated through batch-size dependent behavior of SGD with momentum.
result Momentum operates in two distinct regimes: amplifying stochastic fluctuations at small batch sizes and stabilizing at large batch sizes.
New insights into using momentum for non-convex optimization.
problem Improving training of non-convex models like deep neural networks.
method Developed a Lyapunov analysis of SGD with momentum using stochastic primal averaging.
result Precise conditions under which SGD+M outperforms SGD and optimal hyper-parameter schedules.
Proposes EDM algorithm to accelerate model training in distributed networks.
problem Hindered effectiveness of distributed stochastic optimization algorithms due to data heterogeneity and network sparsity.
method Introduces Exact-Diffusion with Momentum (EDM) algorithm, incorporating momentum techniques to mitigate bias and enhance convergence rate.
result EDM algorithm converges sub-linearly to the optimal solution, radius independent of data heterogeneity, for non-convex objective functions.
Proposes momentum methods for Lie groups, improving on classical algorithms.
problem Optimization on nonlinear spaces, especially Lie groups.
method Generalizes Nesterov's Accelerated Gradient method to Lie groups.
result Demonstrates faster convergence for NAG-like methods on Lie groups.
SQuARM-SGD improves decentralized SGD efficiency with momentum.
problem Efficient decentralized training of large-scale models over networks.
method Fixed local SGD steps with Nesterov's momentum, sparsified and quantized updates, locally computed triggering criterion.
result Convergence rate matches vanilla SGD, momentum improves test performance.
Optimal portfolios are formed by combining momentum, size, and volatility characteristics, enhancing utility for all investors.
problem Estimation error in forming optimal portfolios from characteristics.
method Maximizing an in-sample loss function that is more concave than the utility function, linking weights to characteristics.
result Optimal portfolios with significantly higher certainty equivalents than benchmarks for all investors.
Study shows momentum-based optimizers like Muon and MomentumGD bias towards KKT points in smooth homogeneous models.
problem Understanding the implicit bias of momentum-based optimizers on smooth homogeneous models.
method Analysis of Muon, MomentumGD, Signum, and Adam optimizers under decaying learning rate schedules.
result Momentum-based optimizers approximate steepest descent trajectories and bias towards KKT points of margin maximization problems.
Analysis of momentum methods on quadratic models, showing SGD's superiority.
problem Analysis of stochastic gradient algorithms with momentum on quadratic models.
method Inspired by random matrix theory, exact characterization of loss values.
result Stochastic heavy-ball momentum does not improve over SGD in the strongly convex setting.
New method finds near-optimal solutions for non-convex optimization problems.
problem Finding near-optimal solutions for non-convex optimization problems.
method Riemannian stochastic recursive momentum method
result Achieves a near-optimal complexity of ildeO(ε−3). Study limits of quasi-local angular momentum at infinity of gravitating systems.
problem Understanding limits of quasi-local angular momentum at infinity of gravitating systems.
method Based on optimal isometric embedding and quasilocal mass theory, the study defines and analyzes the limits of quasi-local angular momentum at spatial and null infinity.
result Limits of quasi-local angular momentum are discussed at spatial and null infinity of an isolated gravitating system.
New algorithm accelerates single-pass SGD for generalized linear prediction.
problem Improving single-pass non-quadratic stochastic optimization.
method Data-dependent proximal method incorporating dual-momentum acceleration.
result Momentum acceleration resolves open problem in streaming setting.
New algorithms reduce bilevel optimization complexity to ε^(-1.5).
problem Efficiently solving bilevel optimization problems in machine learning.
method Proposed two new algorithms: one using momentum-based recursive iterations, the other using recursive gradient estimations.
result Achieved computational complexity of ε^(-1.5), significantly faster than previous methods.
Laprop separates Adam's momentum and adaptivity to improve stability and speed.
problem Unnecessary coupling between Adam's momentum and adaptivity leads to instability and divergence.
method Proposes Laprop, a method that decouples momentum and adaptivity.
result Laprop consistently improves speed and stability over Adam on various tasks.
New methods solve optimization problems with heavy-tailed noise, improving upon existing complexity bounds.
problem Optimization problems with heavy-tailed noise and weakly average smoothness.
method Normalized stochastic first-order methods with Polyak, multi-extrapolated, and recursive momentum.
result First-order oracle complexity results for finding approximate stochastic stationary points under heavy-tailed noise.
AdamS uses momentum as a denominator to optimize LLMs efficiently.
problem Optimizing large language models (LLMs) with efficient and effective methods.
method AdamS introduces a novel denominator based on the root of the weighted sum of squares of momentum and current gradient.
result AdamS achieves superior optimization performance with minimal memory and compute requirements.
Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet been proposed for second-order algorithms in nonconvex optimization.In this paper, …
Momentum Stochastic Gradient Descent (MSGD) algorithm has been widely applied to many nonconvex optimization problems in machine learning, e.g., training deep neural networks, variational Bayesian inference, and etc. Despite its empirical success, there is still a lack of theoretical understanding of convergence proper…
Nesterov's momentum trick is famously known for accelerating gradient descent, and has been proven useful in building fast iterative algorithms. However, in the stochastic setting, counterexamples exist and prevent Nesterov's momentum from providing similar acceleration, even if the underlying problem is convex and fin…
New algorithm improves stability of optimization algorithms by adapting step-size.
problem Optimization algorithms' effectiveness is sensitive to step-size hyperparameters.
method Adapts NGN step-size method with momentum to enhance stability.
result Achieves convergence rate of O(1/√K) without restrictive assumptions.
New SGD algorithm finds critical points faster with second-order corrections.
problem Finding critical points in non-convex optimization efficiently.
method Uses Hessian-vector products to correct momentum bias in SGD.
result Finds ε-critical points in O(ε−3) time. Momentum ResNets improve ResNets' memory efficiency.
problem Memory inefficiency in deep residual neural networks (ResNets).
method Adding a momentum term to the forward rule of ResNets to make them invertible.
result Momentum ResNets can learn any linear mapping up to a multiplicative factor, improving memory efficiency.
Study accelerates optimization methods in non-convex problems, but doesn't improve the algorithm's performance.
problem Understanding the behavior of momentum-based acceleration methods in non-convex, high-dimensional landscapes.
method Used dynamical mean field theory to describe the average dynamics of heavy-ball momentum and Nesterov acceleration in a non-convex model.
result Accelerated dynamics but did not improve the algorithm's performance with respect to gradient descent.
New factorial power constants improve optimization convergence rates.
problem Optimization convergence rates depend on various constants.
method Proposes using factorial powers for defining these constants.
result Factorial powers simplify or improve convergence rates of optimization methods.
CoolMomentum combines momentum and Simulated Annealing for deep learning optimization.
problem Global optimization of non-convex functions in deep learning.
method Discretized Langevin dynamics with Simulated Annealing.
result CoolMomentum achieves high accuracy on Resnet-20 on Cifar-10 and Efficientnet-B0 on Imagenet.
New method resolves ambiguity in measuring black hole merger angular momentum.
problem Ambiguity in measuring angular momentum during black hole mergers.
method Quasilocal mass and optimal isometric embedding theory.
result New definition of angular momentum free of supertranslation ambiguity.
Unified algorithm for stochastic optimization with time-varying momentum converges under general conditions.
problem Optimizing functions with time-varying gradients and biases.
method Unified algorithm using a time-varying momentum term.
result Convergence of the unified algorithm under general conditions.
A new accelerated method with simpler momentum update rules.
problem Optimizing parameters in machine learning models.
method Proposes a novel accelerated stochastic gradient method with simpler momentum update rules.
result The method outperforms Sgdm and Adam in practical problems.
This work provides formal guarantees for heuristic optimization methods in machine learning.
problem Lack of theoretical understanding of heuristic optimization methods in machine learning.
method Analysis and formal guarantees for AdaGrad, SGD with exponential and cosine step sizes, and momentum methods.
result First formal guarantees for AdaGrad and SGD variants, including convergence and adaptivity to noise.
This study uses continuous-time analysis to understand how momentum affects the optimisation of diagonal linear networks.
problem The effect of momentum on the optimisation trajectory of gradient descent.
method Leveraging a continuous-time approach to analyze momentum gradient descent with step size γ and momentum parameter β.
result Small values of λ help recover sparse solutions in overparametrised regression settings.
L2GMOM learns financial networks and optimizes momentum strategies.
problem Expensive databases and financial expertise limit network construction accessibility.
method End-to-end machine learning framework (L2GMOM) that learns networks and optimizes trading signals.
result Significant improvement in portfolio profitability and risk control with Sharpe ratio of 1.74.
This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.