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 -functions. We derive Momentum Value Iteration (MoVI), a variation of Value Iteration that incorporates …
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48 results for “momentum values”
Introduces group-valued momentum maps for symplectic fiber bundles.
problem Determining momentum maps for non-classical actions of automorphism groups.
method Develops a general framework for group-valued momentum maps.
result Illustrates the power of group-valued momentum maps with various examples.
Constructibility of momentum maps and linear variation for singular symplectic reduced spacesmath.SG
The paper extends a theorem about momentum maps to singular symplectic spaces.
problem Extending a theorem about momentum maps to singular symplectic spaces.
method Using integral affine stratification and equivariant locally trivial fibrations, the paper extends the linear variation theorem to singular values of the momentum map.
result Cohomology classes of symplectic forms on reduced spaces vary linearly within strata.
Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient . Large values can potentially deliver much larger speedups, but are prone to oscillations and instability; hence one typic…
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…
Customer Momentumq-fin.PR
Customer momentum is a positive relationship between a firm's returns and past returns of its customers.
problem Understanding the relationship between a firm's returns and its customers' past returns.
method Examined customer momentum using a long-short equally-weighted decile portfolio and Fama-French factor models.
result Customer momentum generates significant monthly returns and is statistically significant.
The article examines in some detail the convergence rate and mean-square-error performance of momentum stochastic gradient methods in the constant step-size and slow adaptation regime. The results establish that momentum methods are equivalent to the standard stochastic gradient method with a re-scaled (larger) step-si…
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to , the bundle of vertically adapted linear frames over the bundle of field configurations . Specifically, the generalized field momentum obs…
Momentum speeds up evolutionary processes in machine learning.
problem Accelerating convergence in evolutionary dynamics.
method Combining momentum from machine learning with evolutionary dynamics using information divergences as Lyapunov functions.
result Momentum accelerates convergence of evolutionary dynamics, including the replicator equation and Euclidean gradient descent.
There exist three main approaches to reduction associated to canonical Lie group actions on a symplectic manifold, namely, foliation reduction, introduced by Cartan, Marsden-Weinstein reduction, and optimal reduction, introduced by the authors. When the action is free, proper, and admits a momentum map these three appr…
We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to…
We present a reduction procedure for locally conformally symplectic (LCS) manifolds with an action of a Lie group preserving the conformal structure, with respect to any regular value of the momentum mapping. Under certain conditions, this reduction is compatible with the existence of a locally conformally Kähler struc…
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.
The paper analyzes dynamics of momentum in high dimensions with sparse updates.
problem Theoretical analysis of momentum dynamics in high-dimensional sparse settings.
method Theoretical analysis of two models: least squares with sparse inputs and logistic regression with a rare class.
result Characterization of high-dimensional limits of momentum dynamics and phase structure.
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.
New algorithm reduces risk in online games with limited feedback.
problem Risk-averse learning in repeated unknown games with bandit feedback.
method Proposes a momentum-based algorithm to estimate CVaR using historical cost values.
result Achieves sub-linear regret and outperforms existing methods in numerical experiments.
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization of affine space called a log affine manifold. Using this momentu…
New loss function connects learning rate and momentum.
problem Finding optimal learning rate and momentum empirically.
method Proposes a new information-theoretical loss function.
result Loss, learning rate, and momentum are closely connected.
We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…
The paper explains stock market predictability through a model of heterogeneous beliefs.
problem Understanding and predicting stock market behavior based on news and investor beliefs.
method A discrete-time model of heterogeneous beliefs where some agents receive noisy signals about asset fundamentals.
result Momentum and reversal in stock prices arise from investors' incorrect beliefs about signal accuracy and fundamental values.
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.
Study of closed trajectories in hyperbolic plane with specific curvature constraints.
problem Critical trajectories in hyperbolic plane for a specific energy function.
method Classification of critical trajectories based on momentum causal character, proof of existence of closed trajectories.
result Existence of countably many closed trajectories with time-like momentum.
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.
Minimizing Shortfallq-fin.PM
This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing shortfall generally improves performance ov…
ChatGPT improves momentum strategies by analyzing news data.
problem Improving risk-adjusted returns in systematic investing.
method Combining LLMs with daily equity returns and news data to predict stock momentum.
result LLM-enhanced momentum strategies outperform benchmarks in Sharpe and Sortino ratios.
The paper investigates how target normalization and momentum affect dying ReLUs in neural networks.
problem Understanding and mitigating the dying ReLU problem in neural networks.
method Empirical analysis and theoretical modeling of a discrete-time linear autonomous system.
result Target variance plays a crucial role in the dying ReLU phenomenon, and momentum exacerbates this issue.
Symplectic reduction by abelian subgroups coincides under specific conditions.
problem Conditions for symplectic reduction by abelian subgroups to match.
method Reduction-by-stages framework, nilpotent Lie groups, generic momentum values.
result Symplectomorphic reduced spaces under mild conditions.
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…
Super-acceleration of gradient descent with momentum improves loss function minimization.
problem Minimizing loss functions in machine learning.
method Extending Nesterov acceleration by using gradients at multiple steps ahead.
result Super-acceleration of the momentum algorithm is beneficial for various loss landscapes and tasks.
Proof of local well-posedness for a specific boundary condition in general relativity.
problem Initial boundary value problem in general relativity with umbilic boundary condition.
method Wave coordinates and key observation of momentum constraint validity for umbilic boundaries.
result Local well-posedness established for the initial boundary value problem.
We found that factors decay over time, with momentum fitting best.
problem Understanding how factors decay over time and their impact on performance.
method Derived a hyperbolic decay model for factors, tested against linear and exponential alternatives.
result Momentum exhibits hyperbolic decay, outperforming linear and exponential models.
SGDM accelerates faster than SGD with large batch sizes and permits broader learning rates.
problem Understanding the role of momentum in SGDM and its convergence rates.
method Analysis of SGDM convergence rates under strongly convex settings, including finite-sample rates and asymptotic normality of the averaged estimator.
result SGDM converges faster than SGD with large batch sizes and permits broader learning rates.
CoolMomentum: A Method for Stochastic Optimization by Langevin Dynamics with Simulated Annealingstat.ML
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.
The study finds that factor momentum is significant only at short lags compared to stock momentum.
problem Investigating the relationship between factor momentum and stock momentum.
method Replicated earlier findings and conducted a spanning test controlling for stock momentum and factor exposure.
result Factor momentum is significant only at short lags after controlling for stock momentum and factor exposure.
Develops a gradient flow for Muon optimizer, a method for optimization.
problem Optimization of complex systems with matrix-valued parameters.
method Gradient flow on probability measures induced by regularized Muon optimizer.
result Derives continuous-time limits and proves Hamiltonian dissipation.
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.
This paper re-evaluates hyperparameters for fine-tuning pre-trained models.
problem Current hyperparameter settings for fine-tuning are often ad-hoc and fixed.
method Empirical evaluation of learning rate, batch size, and momentum for fine-tuning.
result Optimal hyperparameters are not only dataset-dependent but also sensitive to domain similarity.
We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found that some submarkets generate the higher momentum returns than other …
Introduces homotopy momentum sections on multisymplectic manifolds.
problem No specific problem stated; focuses on introducing a new concept.
method Introduces a new concept of homotopy momentum sections on multisymplectic manifolds.
result Shows that a gauged nonlinear sigma model with Wess-Zumino term has homotopy momentum section structure.
In a previous article, we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the momentum mapping. We use this construction to prove an analogue of a well-known theorem in the symplectic setting about the reduction of cotangent bundles.
An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) iso…
This paper examines momentum spillover across multiple asset classes using only pricing data.
problem Challenges in studying momentum spillover across diverse asset classes due to lack of common characteristics.
method Utilised a linear and interpretable graph learning model to reveal momentum spillover network.
result Network momentum strategy yields a Sharpe ratio of 1.5 and an annual return of 22%.
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.
The study examines the dynamic behavior of RMSprop and Adam algorithms.
problem Understanding the training loss curve patterns of adaptive gradient algorithms.
method Careful numerical experiments and theoretical explanations using the signGD flow.
result Adam converges smoother and faster when momentum factors are close to each other.
Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to ac…
We give a detailed discussion about existence and uniqueness of Lu's momentum map. More precisely, we introduce the infinitesimal momentum map, and we study its properties. This allows us to describe the theory of reconstruction of the momentum map from the infinitesimal one. We provide the conditions for the uniquenes…
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.
The paper analyzes how momentum affects convergence in stochastic gradient methods.
problem Lack of clear understanding of momentum's impact on convergence and performance.
method Unified analysis of several popular algorithms using the QHM formulation.
result Provides practical guidelines for setting learning rate and momentum parameters.