Scaling Effects and Uncertainty Quantification in Neural Actor Critic Algorithms

• URL: http://arxiv.org/abs/2601.17954v1
• Date: Sun, 25 Jan 2026 19:06:49 GMT
• Title: Scaling Effects and Uncertainty Quantification in Neural Actor Critic Algorithms
• Authors: Nikos Georgoudios, Konstantinos Spiliopoulos, Justin Sirignano,
• Abstract summary: We investigate the neural Actor Critic algorithm using shallow neural networks for both the Actor and Critic models.<n>We compare the convergence properties of the network outputs under various scaling schemes as the network width and the number of training steps tend to infinity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the neural Actor Critic algorithm using shallow neural networks for both the Actor and Critic models. The focus of this work is twofold: first, to compare the convergence properties of the network outputs under various scaling schemes as the network width and the number of training steps tend to infinity; and second, to provide precise control of the approximation error associated with each scaling regime. Previous work has shown convergence to ordinary differential equations with random initial conditions under inverse square root scaling in the network width. In this work, we shift the focus from convergence speed alone to a more comprehensive statistical characterization of the algorithm's output, with the goal of quantifying uncertainty in neural Actor Critic methods. Specifically, we study a general inverse polynomial scaling in the network width, with an exponent treated as a tunable hyperparameter taking values strictly between one half and one. We derive an asymptotic expansion of the network outputs, interpreted as statistical estimators, in order to clarify their structure. To leading order, we show that the variance decays as a power of the network width, with an exponent equal to one half minus the scaling parameter, implying improved statistical robustness as the scaling parameter approaches one. Numerical experiments support this behavior and further suggest faster convergence for this choice of scaling. Finally, our analysis yields concrete guidelines for selecting algorithmic hyperparameters, including learning rates and exploration rates, as functions of the network width and the scaling parameter, ensuring provably favorable statistical behavior.

Related papers

• A Mean-Field Analysis of Neural Stochastic Gradient Descent-Ascent for Functional Minimax Optimization [90.87444114491116]
  This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparametricized two-layer neural networks. We address (i) the convergence of the gradient descent-ascent algorithm and (ii) the representation learning of the neural networks. Results show that the feature representation induced by the neural networks is allowed to deviate from the initial one by the magnitude of $O(alpha-1)$, measured in terms of the Wasserstein distance.
  arXiv  Detail & Related papers  (2024-04-18T16:46:08Z)
• Convergence Guarantees of Overparametrized Wide Deep Inverse Prior [1.5362025549031046]
  Inverse Priors is an unsupervised approach to transform a random input into an object whose image under the forward model matches the observation. We provide overparametrization bounds under which such network trained via continuous-time gradient descent will converge exponentially fast with high probability. This work is thus a first step towards a theoretical understanding of overparametrized DIP networks, and more broadly it participates to the theoretical understanding of neural networks in inverse problem settings.
  arXiv  Detail & Related papers  (2023-03-20T16:49:40Z)
• Semantic Strengthening of Neuro-Symbolic Learning [85.6195120593625]
  Neuro-symbolic approaches typically resort to fuzzy approximations of a probabilistic objective. We show how to compute this efficiently for tractable circuits. We test our approach on three tasks: predicting a minimum-cost path in Warcraft, predicting a minimum-cost perfect matching, and solving Sudoku puzzles.
  arXiv  Detail & Related papers  (2023-02-28T00:04:22Z)
• On the Neural Tangent Kernel Analysis of Randomly Pruned Neural Networks [91.3755431537592]
  We study how random pruning of the weights affects a neural network's neural kernel (NTK) In particular, this work establishes an equivalence of the NTKs between a fully-connected neural network and its randomly pruned version.
  arXiv  Detail & Related papers  (2022-03-27T15:22:19Z)
• Wasserstein Flow Meets Replicator Dynamics: A Mean-Field Analysis of Representation Learning in Actor-Critic [137.04558017227583]
  Actor-critic (AC) algorithms, empowered by neural networks, have had significant empirical success in recent years. We take a mean-field perspective on the evolution and convergence of feature-based neural AC. We prove that neural AC finds the globally optimal policy at a sublinear rate.
  arXiv  Detail & Related papers  (2021-12-27T06:09:50Z)
• Training Integrable Parameterizations of Deep Neural Networks in the Infinite-Width Limit [0.0]
  Large-width dynamics has emerged as a fruitful viewpoint and led to practical insights on real-world deep networks. For two-layer neural networks, it has been understood that the nature of the trained model radically changes depending on the scale of the initial random weights. We propose various methods to avoid this trivial behavior and analyze in detail the resulting dynamics.
  arXiv  Detail & Related papers  (2021-10-29T07:53:35Z)
• Bayesian Attention Belief Networks [59.183311769616466]
  Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. This paper introduces Bayesian attention belief networks, which construct a decoder network by modeling unnormalized attention weights. We show that our method outperforms deterministic attention and state-of-the-art attention in accuracy, uncertainty estimation, generalization across domains, and adversarial attacks.
  arXiv  Detail & Related papers  (2021-06-09T17:46:22Z)
• Nonasymptotic theory for two-layer neural networks: Beyond the bias-variance trade-off [10.182922771556742]
  We present a nonasymptotic generalization theory for two-layer neural networks with ReLU activation function. We show that overparametrized random feature models suffer from the curse of dimensionality and thus are suboptimal.
  arXiv  Detail & Related papers  (2021-06-09T03:52:18Z)
• Efficient and Sparse Neural Networks by Pruning Weights in a Multiobjective Learning Approach [0.0]
  We propose a multiobjective perspective on the training of neural networks by treating its prediction accuracy and the network complexity as two individual objective functions. Preliminary numerical results on exemplary convolutional neural networks confirm that large reductions in the complexity of neural networks with neglibile loss of accuracy are possible.
  arXiv  Detail & Related papers  (2020-08-31T13:28:03Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.