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.
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.
Combines MALA and Adam for efficient uncertainty quantification in deep learning.
problem Uncertainty estimation in deep neural networks.
method Integrates Metropolis Adjusted Langevin Algorithm (MALA) with momentum-based optimization (Adam) for efficient sampling from posterior distributions.
result The algorithm approximates the Gibbs posterior in total variation distance and efficiently quantifies epistemic uncertainty.
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.
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.
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.
Efficient momentum-based methods for reinforcement learning with improved sample complexity.
problem Efficient reinforcement learning algorithms for non-concave performance functions.
method Adaptive momentum-based policy gradient methods using variance reduction and importance sampling techniques.
result Both IS-MBPG and HA-MBPG reach the best known sample complexity of O(ε−3) for finding an ε-stationary point. Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum parameter m which is always suggested to be set to less than 1. Although the choice…
To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we start by …
Improved time complexity for parallel stochastic optimization in heterogeneous systems.
problem Time complexity in parallel stochastic optimization for large-scale machine learning models.
method Proposes Rennala MVR, a variance-reduced extension of Rennala SGD based on momentum-based variance reduction.
result Variance reduction improves time complexity in relevant parameter regimes for parallel stochastic optimization in heterogeneous systems.
Unified framework for analyzing batch updating methods with noisy gradients.
problem Analyzing convergence of batch updating methods with noisy gradients and approximations.
method Unified framework using convergence of stochastic processes.
result Establishes a general theorem for most known convergence results.
MiMuon optimizer improves generalization for large models by reducing generalization error.
problem Improving generalization of Muon optimizer for large models.
method Enhanced Muon optimizer using orthogonalization of gradient, proving lower generalization error.
result MiMuon optimizer has a lower generalization error of O(N1) compared to Muon's O(NκT1). 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.
This paper revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a coordinate descent characterization, IPS can be slightly modified to deliver coefficient estimates, and from a majorization-minimizat…
The paper studies momentum-based minimization for Ginzburg-Landau on Euclidean spaces and graphs.
problem Minimizing the Ginzburg-Landau functional on Euclidean spaces and graphs.
method Momentum-based minimization using a convex-concave splitting-based FISTA-type time discretization.
result Momentum can lead to faster convergence if the time step size is large but not too large.
A fast method for training linear classifiers maximizes margins.
problem Training linear classifiers with maximum margins.
method Momentum-based gradient method derived from convex dual with Nesterov acceleration.
result Exponentially faster convergence rate compared to standard methods.
AdamP optimizes momentum-based optimizers for scale-invariant weights, improving model performance.
problem Premature decay of effective step sizes in momentum-based optimizers for scale-invariant weights.
method Proposes SGDP and AdamP to eliminate the radial component at each optimizer step, preserving convergence properties.
result Uniform gains across multiple benchmarks, improving model performance.
This paper studies accelerations in Q-learning algorithms. We propose an accelerated target update scheme by incorporating the historical iterates of Q functions. The idea is conceptually inspired by the momentum-based accelerated methods in the optimization theory. Conditions under which the proposed accelerated algor…
Simplified optimization for structured matrices in deep learning.
problem Computational challenges in Riemannian submanifold optimization for structured symmetric positive-definite matrices.
method Proposed a generalized Riemannian normal coordinates that dynamically orthonormalizes the metric and converts the problem into an unconstrained Euclidean space problem.
result Simplified existing approaches for structured covariances and developed matrix-inverse-free 2nd-order optimizers for deep learning with low precision.
We take a Hamiltonian-based perspective to generalize Nesterov's accelerated gradient descent and Polyak's heavy ball method to a broad class of momentum methods in the setting of (possibly) constrained minimization in Euclidean and non-Euclidean normed vector spaces. Our perspective leads to a generic and unifying non…
Arguably, the two most popular accelerated or momentum-based optimization methods in machine learning are Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different discretizations of a particular second order differential equation with friction. Such connections with continuous-time dyna…
Improved optimization guarantees for deep learning models with Nesterov acceleration.
problem Optimization in non-convex deep learning landscapes.
method Analysis of Nesterov acceleration in benignly non-convex landscapes.
result Identical guarantees can be obtained in optimization problems with weak geometric assumptions, especially in overparametrized deep learning.
New bounds for model generalization under deterministic gradient descent.
problem Establishing generalization bounds for models trained with gradient descent methods.
method PAC-Bayesian bounds for deterministic optimisation algorithms.
result Fully computable bounds that depend on initial distribution and Hessian.
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.
AB dynamically scales gradients to mitigate asynchronous training delays.
problem Gradient delay in asynchronous training reduces model performance.
method Adaptive Braking (AB) dynamically scales gradients based on alignment.
result AB enables training with up to 32 update steps of delay without accuracy loss.
New optimization method combines gradient clipping and non-Euclidean smoothness.
problem Improving optimization in non-Euclidean spaces for machine learning.
method Hybrid of steepest descent and conditional gradient, incorporating weight decay.
result Achieves optimal convergence rate and demonstrates effectiveness in deep learning.
We accelerate PMD algorithms for reinforcement learning using functional methods.
problem Improving reinforcement learning algorithms for large-scale optimization.
method Proposed a momentum-based update for PMD algorithms leveraging duality.
result The proposed method accelerates reinforcement learning algorithms.
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.
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.
While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that there exists a convex loss function for which the stability gap fo…
Paper tackles Hessian/Jacobian-free stochastic bilevel optimization with O(ε−1.5) complexity.
problem Nonconvex-strongly-convex bilevel optimization problem.
method FdeHBO optimizer with finite-difference Hessian/Jacobian-vector approximation and momentum.
result FdeHBO achieves O(ε−1.5) iterations for ε-accurate stationary point. 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.
Momentum-based acceleration of stochastic gradient descent (SGD) is widely used in deep learning. We propose the quasi-hyperbolic momentum algorithm (QHM) as an extremely simple alteration of momentum SGD, averaging a plain SGD step with a momentum step. We describe numerous connections to and identities with other alg…
Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require c…
Efficient algorithm for Hadamard decomposition of matrices.
problem Decomposing matrices into low-rank factors efficiently.
method Alternating optimization with SVD-inspired initialization and momentum.
result Significantly improved performance compared to existing methods.
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.
Paper develops algorithms for nonsmooth, nonconvex statistical learning problems.
problem Nonsmooth and nonconvex objectives in statistical learning.
method Bregman-surrogate algorithm framework, including local linear approximation, mirror descent, iterative thresholding, DC programming.
result Global convergence rates for nonconvex and nonsmooth objectives in high dimensions.
New sampling method on Lie groups converges quickly.
problem Sampling on non-Euclidean Lie groups.
method Kinetic Langevin dynamics with noise added.
result Exponential convergence rate proved under W2 distance. New insights into training machine learning models with momentum.
problem Lack of theoretical understanding on the generalization error of momentum-based methods.
method Analyzed modified momentum-based update rule (SGDEM) for smooth Lipschitz loss functions.
result SGDEM admits an upper-bound on the generalization error for smooth Lipschitz loss functions.
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.
A new Adamize method improves multi-objective recommender systems.
problem Improving recommendation systems with multiple conflicting objectives.
method Developed a multi-objective model-agnostic Adamize method that corrects and stabilizes gradients.
result Significant improvements in recommendation systems, measured by hypervolume, coverage, and spacing.
AdEMAMix optimizer improves model performance and convergence speed.
problem Suboptimal use of single EMA in momentum-based optimizers.
method Proposes AdEMAMix, a modified Adam optimizer with a mixture of two EMAs.
result Empirically shows gradients can remain relevant for tens of thousands of steps, leading to faster convergence and lower minima.
Integrates momentum into RNNs to improve training.
problem Vanishing gradient in RNNs during training.
method Established connection between RNN dynamics and GD, integrated momentum.
result MomentumRNNs alleviate vanishing gradient issue and improve convergence.
FGD reduces noisy gradient variance in SGD for neural networks.
problem Noisy and unreliable gradient estimation in SGD for deep learning.
method Solves an adaptive filtering problem to consistently estimate the local gradient.
result Significantly reduces gradient variance and accelerates convergence.
New analysis reveals batch size effects on stochastic conditional gradient methods.
problem Understanding the role of batch size in stochastic conditional gradient methods.
method Deriving a new analysis focusing on momentum-based stochastic conditional gradient algorithms (e.g., Scion).
result Increasing batch size initially improves optimization accuracy but can degrade performance beyond a critical threshold.
DreamPropeller accelerates text-to-3D generation by 4.7x with minimal loss in quality.
problem Long generation times in text-to-3D generation algorithms degrade user experience.
method DreamPropeller uses Picard iterations generalized for non-ODE paths to accelerate parallel sampling.
result Empirically achieves up to 4.7x speedup with negligible quality loss.
Mime algorithm improves federated learning by adapting centralized methods.
problem Mitigating client drift in federated learning.
method Combines control variates and server-level statistics to adapt centralized algorithms to federated learning.
result Mime outperforms any centralized method in federated learning.
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.