AdaX improves Adam by exponentially accumulating past gradients, leading to better performance in machine learning tasks.
problem Adam's fast convergence can lead to local minimums in non-convex problems.
method AdaX exponentially accumulates past gradients to adaptively tune the learning rate.
result AdaX outperforms Adam in various machine learning tasks, including computer vision and natural language processing.
In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragmén-Lindelöf principle we prove exponential decay of the eigenfunctions corresponding to the non-threshold eigenvalues of t…
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.
Ridge regression linked to Poisson resetting in statistical physics.
problem Understanding and extending ridge regularization in machine learning.
method Connecting stochastic resetting from statistical physics with ridge regularization in machine learning, using renewal processes.
result Exact filter identities for ridge regularization in various reset laws, including exponential and non-exponential.
In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiase…
SLEDGE algorithm reduces gradient computation errors in optimization.
problem Accumulated errors in gradient estimation methods for large-scale optimization.
method Single-loop method for finite-sum nonconvex optimization without periodic gradient refresh.
result Achieves nearly optimal gradient complexity and second-order optimality.
AdaGrad fails to adapt to Hölder-smoothness in composite optimization problems.
problem AdaGrad's convergence rate is suboptimal for composite objectives.
method Exhibited a simple one-dimensional convex problem to highlight AdaGrad's limitations.
result AdaGrad does not achieve the classical convergence rate for Hölder-smooth objectives.
This paper deals with bandit online learning problems involving feedback of unknown delay that can emerge in multi-armed bandit (MAB) and bandit convex optimization (BCO) settings. MAB and BCO require only values of the objective function involved that become available through feedback, and are used to estimate the gra…
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…
GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.
problem Fixed learning rate in AdaGrad leads to step size decrease over time.
method Introduces GradaGrad, which grows or shrinks the learning rate based on a different accumulation in the denominator.
result GradaGrad achieves similar convergence rates as AdaGrad and demonstrates non-monotone adaptation.
Behavior cloning training instabilities amplified by SGD noise over long horizons.
problem Training instabilities in behavior cloning with deep neural networks.
method Empirical dissection of minibatch SGD updates and their effects on long-horizon rewards.
result Exponential moving average (EMA) of iterates effectively mitigates gradient variance amplification (GVA).
This work addresses the instability in asynchronous data parallel optimization. It does so by introducing a novel distributed optimizer which is able to efficiently optimize a centralized model under communication constraints. The optimizer achieves this by pushing a normalized sequence of first-order gradients to a pa…
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…
A new correction term improves sample efficiency in deep reinforcement learning.
problem Momentum accumulation in TD learning leads to doubly stale gradients.
method Proposed a correction term to address the issue of doubly stale gradients.
result Improves sample efficiency in policy evaluation.
New inequalities help optimize first-order algorithms for statistical risk analysis.
problem Optimizing first-order iterative algorithms for statistical risk analysis.
method Introducing basic inequalities that connect implicit and explicit regularization.
result The basic inequalities translate the number of iterations into an effective regularization coefficient.
Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In…
A new method improves training speed and robustness for deep learning models.
problem Training deep learning models with heavy-tailed gradient noise.
method Per-sample gradient clipping combined with SGD.
result PS-Clip-SGD achieves optimal convergence rates and high-probability guarantees.
Paper explores low-precision SGLD for neural networks, reducing costs without sacrificing performance.
problem Infeasibility of low-precision sampling in large-scale scenarios.
method Developed low-precision SGLD with quantization function and full-precision gradient accumulators.
result Low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits.
We look at how asset exchange models can be mapped to random iterated function systems (IFS) giving new insights into the dynamics of wealth accumulation in such models. In particular, we focus on the "yard-sale" (winner gets a random fraction of the poorer players wealth) and the "theft-and-fraud" (winner gets a rando…
Proposes reducing random error in stochastic optimization by variance regularization.
problem Random error accumulation in stochastic optimization algorithms.
method Regularizes learning-rate based on mini-batch variances.
result Speeds up convergence and stabilizes stochastic optimization.
Jones polynomials for knots and links with many crossings calculated efficiently.
problem Computing Jones polynomials for knots and links with a large number of crossings.
method Calculating Tutte polynomials for associated graphs and evaluating with specific substitutions.
result Jones polynomials for knots and links with many crossings calculated efficiently.
VCoTTA uses variational Bayesian methods to adapt models under continuous domain shifts.
problem Error accumulation in continual test-time adaptation.
method VCoTTA employs variational Bayesian techniques to update a Bayesian Neural Network (BNN) during testing, combining priors from source and teacher models.
result VCoTTA effectively mitigates error accumulation in CTTA, as shown by experimental results on three datasets.
We consider a priori generalization bounds developed in terms of cross-validation estimates and the stability of learners. In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general function of n independent random variables. Next, under some reasonable notion of s…
We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize 1/L satisfies the $L…
Gradient-free optimizers are ineffective on barren plateaus in quantum computing.
problem Effect of barren plateaus on gradient-free optimization in quantum computing.
method Numerical simulations and theoretical analysis of gradient-free optimization algorithms.
result Gradient-free optimizers are not effective in barren plateau landscapes due to exponentially suppressed cost function differences.
The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\in \C\{z,w\}$, using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac ph…
FedSel uses local differential privacy to protect data privacy in federated SGD.
problem Privacy leakage from gradients in federated SGD.
method Two-stage framework with top-k dimension selection and gradient accumulation.
result FedSel reduces privacy leakage by privately selecting important dimensions.
In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For …
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
Accelerated gradient method's stability deteriorates exponentially with steps.
problem Algorithmic stability of Nesterov's accelerated gradient method.
method Analysis of two notions of algorithmic stability for Nesterov's accelerated gradient method.
result Stability of Nesterov's accelerated method deteriorates exponentially with the number of gradient steps.
Reinforcement learning for embodied agents is a challenging problem. The accumulated reward to be optimized is often a very rugged function, and gradient methods are impaired by many local optimizers. We demonstrate, in an experimental setting, that incorporating an intrinsic reward can smoothen the optimization landsc…
MSTGD optimizes gradient descent with stratified sampling for faster convergence.
problem Fluctuation in gradient expectation and variance between iterations.
method Memory Stochastic Stratified Gradient Descent (MSTGD) with stratified sampling and variance reduction.
result MSTGD achieves an exponential convergence rate independent of dataset size and batch size.
EGAB algorithms improve online portfolio selection.
problem Online portfolio selection problem.
method Generalized exponentiated gradient (EG) updates with Alpha-Beta divergence regularization.
result EGAB algorithms enhance portfolio performance, especially with transaction costs.
A new method for MARL with partial observations reduces communication overhead.
problem Inefficient MARL algorithms in large-scale problems due to state and action information sharing.
method Distributed zeroth-order policy optimization with local policy gradient estimation using consensus.
result The method converges to a policy that is a stationary point of the global objective function.
Efforts to reduce the numerical precision of computations in deep learning training have yielded systems that aggressively quantize weights and activations, yet employ wide high-precision accumulators for partial sums in inner-product operations to preserve the quality of convergence. The absence of any framework to an…
Introduces a new theoretical framework for exponential smoothing.
problem Theoretical foundation and robustness of simple exponential smoothing.
method Stochastic gradient ascent to optimize Gaussian log-likelihood functions.
result Simple exponential smoothing converges to the trend of a trend-stationary process.
Gradient descent can take exponentially long to escape saddle points in 2D.
problem Worst-case inefficiency of gradient descent in non-convex optimization.
method Analysis of gradient descent's performance on 2D functions.
result Gradient descent can take exponentially long to escape saddle points.
Flow-based models generate data with improved theoretical guarantees.
problem Theoretical analysis of flow-based generative models.
method Proximal gradient descent in Wasserstein space for JKO flow model.
result KL guarantee of data generation by JKO flow model is O(ε2). The paper proposes a method to train time-varying generative models using natural gradients.
problem Training time-varying generative models efficiently and accurately.
method Projecting generative model parameters onto an exponential family manifold and optimizing using natural gradient descent.
result The proposed method efficiently approximates the natural gradient and can be applied to various exponential family models.
New method speeds up lifelong learning of complex tasks.
problem Catastrophic forgetting in lifelong learning.
method Directly trains lifelong function approximators via policy gradients.
result Faster convergence and better policies achieved.
STORM-PG uses momentum for faster policy gradient updates.
problem Improving policy gradient methods for reinforcement learning.
method Introduces STORM-PG, a SARAH-based algorithm with exponential moving average.
result Achieves O(1/ε3) sample complexity, matching best-known rate. There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, …
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 paper revisits optimal investment strategies for defined contribution pension schemes using forward preferences.
problem Optimal investment strategies derived from backward models are not time-consistent and sub-optimal in real scenarios.
method Introduces forward preferences and solves optimal investment strategies for defined contribution pension schemes.
result Constructs optimal investment strategies for defined contribution pension schemes using forward preferences.
Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure by fitting an exponential family model in a Reprod…
Full-batch GD achieves generalization close to any stationary point with fewer assumptions.
problem Generalization and excess risk bounds for smooth losses, including non-Lipschitz and nonconvex cases.
method Path-dependent analysis of GD's generalization error, focusing on optimization error and stability.
result Generalization error is tightly bound in terms of optimization error and iteration count, bypassing common assumptions.