Optimal Learning via Moderate Deviations Theory

• URL: http://arxiv.org/abs/2305.14496v3
• Date: Tue, 13 Feb 2024 20:37:10 GMT
• Title: Optimal Learning via Moderate Deviations Theory
• Authors: Arnab Ganguly, Tobias Sutter
• Abstract summary: We develop a systematic construction of highly accurate confidence intervals by using a moderate deviation principle-based approach. It is shown that the proposed confidence intervals are statistically optimal in the sense that they satisfy criteria regarding exponential accuracy, minimality, consistency, mischaracterization probability, and eventual uniformly most accurate (UMA) property.
• Score: 4.6930976245638245
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming problem or various SDE models. More precisely, we develop a systematic construction of highly accurate confidence intervals by using a moderate deviation principle-based approach. It is shown that the proposed confidence intervals are statistically optimal in the sense that they satisfy criteria regarding exponential accuracy, minimality, consistency, mischaracterization probability, and eventual uniformly most accurate (UMA) property. The confidence intervals suggested by this approach are expressed as solutions to robust optimization problems, where the uncertainty is expressed via the underlying moderate deviation rate function induced by the data-generating process. We demonstrate that for many models these optimization problems admit tractable reformulations as finite convex programs even when they are infinite-dimensional.

Related papers

• Statistical Inference for Temporal Difference Learning with Linear Function Approximation [62.69448336714418]
  Temporal Difference (TD) learning, arguably the most widely used for policy evaluation, serves as a natural framework for this purpose. In this paper, we study the consistency properties of TD learning with Polyak-Ruppert averaging and linear function approximation, and obtain three significant improvements over existing results.
  arXiv  Detail & Related papers  (2024-10-21T15:34:44Z)
• Probabilistic Iterative Hard Thresholding for Sparse Learning [2.5782973781085383]
  We present an approach towards solving expectation objective optimization problems with cardinality constraints. We prove convergence of the underlying process, and demonstrate the performance on two Machine Learning problems.
  arXiv  Detail & Related papers  (2024-09-02T18:14:45Z)
• Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization [29.24821214671497]
  Training machine learning and statistical models often involve optimizing a data-driven risk criterion. We propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations.
  arXiv  Detail & Related papers  (2024-01-28T21:19:15Z)
• High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization [16.38026811561888]
  This paper introduces a novel inference method focused on constructing confidence intervals with efficient computation and fast convergence to the nominal level. Our method requires minimal additional computation and memory beyond the standard updating of estimates, making the inference process almost cost-free.
  arXiv  Detail & Related papers  (2024-01-17T17:11:45Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Integrated Conditional Estimation-Optimization [6.037383467521294]
  Many real-world optimization problems uncertain parameters with probability can be estimated using contextual feature information. In contrast to the standard approach of estimating the distribution of uncertain parameters, we propose an integrated conditional estimation approach. We show that our ICEO approach is theally consistent under moderate conditions.
  arXiv  Detail & Related papers  (2021-10-24T04:49:35Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• CoinDICE: Off-Policy Confidence Interval Estimation [107.86876722777535]
  We study high-confidence behavior-agnostic off-policy evaluation in reinforcement learning. We show in a variety of benchmarks that the confidence interval estimates are tighter and more accurate than existing methods.
  arXiv  Detail & Related papers  (2020-10-22T12:39:11Z)
• Robust, Accurate Stochastic Optimization for Variational Inference [68.83746081733464]
  We show that common optimization methods lead to poor variational approximations if the problem is moderately large. Motivated by these findings, we develop a more robust and accurate optimization framework by viewing the underlying algorithm as producing a Markov chain.
  arXiv  Detail & Related papers  (2020-09-01T19:12:11Z)

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.