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LaProp: Separating Momentum and Adaptivity in Adam (2002.04839v3)

Published 12 Feb 2020 in cs.LG and stat.ML

Abstract: We identity a by-far-unrecognized problem of Adam-style optimizers which results from unnecessary coupling between momentum and adaptivity. The coupling leads to instability and divergence when the momentum and adaptivity parameters are mismatched. In this work, we propose a method, Laprop, which decouples momentum and adaptivity in the Adam-style methods. We show that the decoupling leads to greater flexibility in the hyperparameters and allows for a straightforward interpolation between the signed gradient methods and the adaptive gradient methods. We experimentally show that Laprop has consistently improved speed and stability over Adam on a variety of tasks. We also bound the regret of Laprop on a convex problem and show that our bound differs from that of Adam by a key factor, which demonstrates its advantage.

Citations (17)

Summary

  • The paper introduces LaProp, an adaptive optimizer that decouples momentum from adaptivity, enhancing stability and flexibility in hyperparameter settings.
  • It presents a theoretical framework with a convergence proof that distinguishes LaProp from Adam and AMSGrad, particularly in handling noisy environments.
  • Extensive experiments across tasks like neural style transfer, deep networks, transformers, and reinforcement learning demonstrate LaProp's superior performance.

Overview of "LaProp: Separating Momentum and Adaptivity in Adam"

The paper in question introduces LaProp, an adaptive optimization algorithm that decouples momentum and adaptivity, thus addressing a potential issue in Adam-style optimizers. This decoupling provides increased flexibility in hyperparameter settings, enabling effective interpolation between signed gradient methods and adaptive gradient methods.

Key Contributions

  1. Algorithm Proposition: LaProp enhances stability and flexibility compared to Adam, maintaining the same number of hyperparameters and allowing direct application of Adam’s settings. The paper demonstrates improved performance, particularly in noisy and unstable environments.
  2. Conceptual Extension: The authors extend existing frameworks for understanding optimization algorithms, presenting a model that includes LaProp as a subclass—something not captured by previous frameworks focused on Adam.
  3. Theoretical Analysis: The paper provides a convergence proof for LaProp, highlighting a distinct factor that differentiates it from Adam and AMSGrad, which limits their flexibility.

Experimental Insights

The paper includes extensive experimental evaluations, showcasing LaProp’s advantages across various tasks:

  • Rosenbrock Loss: In scenarios with increasing noise, LaProp outperforms Adam and AMSGrad, maintaining stability across broader settings.
  • Neural Style Transfer: LaProp achieves superior convergence and stability compared to Adam, even without hyperparameter adjustments.
  • Extremely Deep Networks: LaProp exhibits resilience in training very deep fully connected networks, demonstrating robustness against pathological issues typical in such scenarios.
  • Transformers: On tasks such as IWSLT14 and RoBERTa pretraining, LaProp competes favorably with Adam, achieving faster optimization and overcoming issues without requiring warm-up schedules.
  • Reinforcement Learning: LaProp shows earlier learning initiation and faster high-performance attainment in Atari2600 games compared to Adam, suggesting more aggressive exploration capabilities.

Theoretical Implications

The LaProp algorithm modifies the traditional coupling of momentum and gradient adaptivity seen in Adam. This allows for a broader range of stable hyperparameter settings, potentially leading to higher optimization performance without risking divergence due to improperly matched parameters.

Future Directions

Speculation on the algorithm’s future denotes significant potential for enhancing optimization practices in deep learning:

  • Hyperparameter Exploration: LaProp's decoupling aspect may warrant further exploration into dynamic hyperparameter tuning strategies that can be adaptive to task-specific characteristics.
  • Broader Applicability: It might benefit broader tasks in industrial applications where stability is critical, potentially extending to complex models in varied environments beyond what is traditionally feasible with Adam.

Ultimately, LaProp offers a promising alternative to traditional adaptive optimizers, with solid experimental backing and potential for further advancements in AI optimization methodologies. The flexibility offered by this decoupling is a notable step towards more resilient and adaptive learning algorithms in the field of machine learning.

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