Unbiased Gradient Estimation for Distributionally Robust Learning

• URL: http://arxiv.org/abs/2012.12367v1
• Date: Tue, 22 Dec 2020 21:35:03 GMT
• Title: Unbiased Gradient Estimation for Distributionally Robust Learning
• Authors: Soumyadip Ghosh and Mark Squillante
• Abstract summary: We consider a new approach based on distributionally robust learning (DRL) that applies gradient descent to the inner problem. Our algorithm efficiently estimates gradient gradient through multi-level Monte Carlo randomization.
• Score: 2.1777837784979277
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Seeking to improve model generalization, we consider a new approach based on distributionally robust learning (DRL) that applies stochastic gradient descent to the outer minimization problem. Our algorithm efficiently estimates the gradient of the inner maximization problem through multi-level Monte Carlo randomization. Leveraging theoretical results that shed light on why standard gradient estimators fail, we establish the optimal parameterization of the gradient estimators of our approach that balances a fundamental tradeoff between computation time and statistical variance. Numerical experiments demonstrate that our DRL approach yields significant benefits over previous work.

Related papers

• Differentially Private Optimization with Sparse Gradients [60.853074897282625]
  We study differentially private (DP) optimization problems under sparsity of individual gradients. Building on this, we obtain pure- and approximate-DP algorithms with almost optimal rates for convex optimization with sparse gradients.
  arXiv  Detail & Related papers  (2024-04-16T20:01:10Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• Scalable method for Bayesian experimental design without integrating over posterior distribution [0.0]
  We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems. A-optimality is a widely used and easy-to-interpret criterion for Bayesian experimental design. This study presents a novel likelihood-free approach to the A-optimal experimental design.
  arXiv  Detail & Related papers  (2023-06-30T12:40:43Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
  We consider the task of heavy-tailed statistical estimation given streaming $p$ samples. We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
  arXiv  Detail & Related papers  (2021-08-25T21:30:27Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• Tighter Bounds on the Log Marginal Likelihood of Gaussian Process Regression Using Conjugate Gradients [19.772149500352945]
  We show that approximate maximum likelihood learning of model parameters by maximising our lower bound retains many of the sparse variational approach benefits. In experiments, we show improved predictive performance with our model for a comparable amount of training time compared to other conjugate gradient based approaches.
  arXiv  Detail & Related papers  (2021-02-16T17:54:59Z)
• Beyond variance reduction: Understanding the true impact of baselines on policy optimization [24.09670734037029]
  We show that learning dynamics are governed by the curvature of the loss function and the noise of the gradient estimates. We present theoretical results showing that, at least for bandit problems, curvature and noise are not sufficient to explain the learning dynamics.
  arXiv  Detail & Related papers  (2020-08-31T17:52:09Z)
• Extrapolation for Large-batch Training in Deep Learning [72.61259487233214]
  We show that a host of variations can be covered in a unified framework that we propose. We prove the convergence of this novel scheme and rigorously evaluate its empirical performance on ResNet, LSTM, and Transformer.
  arXiv  Detail & Related papers  (2020-06-10T08:22:41Z)
• Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling [0.0]
  We propose a new optimization algorithm for Bayesian inference based multilevel Monte Carlo (MLMC) methods. Our numerical results confirm considerable computational savings compared to the conventional estimators.
  arXiv  Detail & Related papers  (2020-01-14T09:14:24Z)

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.