Online Statistical Inference in Decision-Making with Matrix Context

• URL: http://arxiv.org/abs/2212.11385v2
• Date: Fri, 18 Apr 2025 19:22:45 GMT
• Title: Online Statistical Inference in Decision-Making with Matrix Context
• Authors: Qiyu Han, Will Wei Sun, Yichen Zhang,
• Abstract summary: We propose an online procedure to conduct statistical inference with adaptively collected data.<n>Standard low-rank estimators are biased and cannot be obtained in a sequential manner.<n>Existing approaches in sequential decision-making algorithms fail to account for the low-rankness and are also biased.
• Score: 5.2071564436846245
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The study of online decision-making problems that leverage contextual information has drawn notable attention due to their significant applications in fields ranging from healthcare to autonomous systems. In modern applications, contextual information can be rich and is often represented as a matrix. Moreover, while existing online decision algorithms mainly focus on reward maximization, less attention has been devoted to statistical inference. To address these gaps, in this work, we consider an online decision-making problem with a matrix context where the true model parameters have a low-rank structure. We propose a fully online procedure to conduct statistical inference with adaptively collected data. The low-rank structure of the model parameter and the adaptive nature of the data collection process make this difficult: standard low-rank estimators are biased and cannot be obtained in a sequential manner while existing inference approaches in sequential decision-making algorithms fail to account for the low-rankness and are also biased. To overcome these challenges, we introduce a new online debiasing procedure to simultaneously handle both sources of bias. Our inference framework encompasses both parameter inference and optimal policy value inference. In theory, we establish the asymptotic normality of the proposed online debiased estimators and prove the validity of the constructed confidence intervals for both inference tasks. Our inference results are built upon a newly developed low-rank stochastic gradient descent estimator and its convergence result, which are also of independent interest.

Related papers

• Adaptive Conformal Inference by Betting [51.272991377903274]
  We consider the problem of adaptive conformal inference without any assumptions about the data generating process. Existing approaches for adaptive conformal inference are based on optimizing the pinball loss using variants of online gradient descent. We propose a different approach for adaptive conformal inference that leverages parameter-free online convex optimization techniques.
  arXiv  Detail & Related papers  (2024-12-26T18:42:08Z)
• Optimal Baseline Corrections for Off-Policy Contextual Bandits [61.740094604552475]
  We aim to learn decision policies that optimize an unbiased offline estimate of an online reward metric. We propose a single framework built on their equivalence in learning scenarios. Our framework enables us to characterize the variance-optimal unbiased estimator and provide a closed-form solution for it.
  arXiv  Detail & Related papers  (2024-05-09T12:52:22Z)
• Pessimistic Causal Reinforcement Learning with Mediators for Confounded Offline Data [17.991833729722288]
  We propose a novel policy learning algorithm, PESsimistic CAusal Learning (PESCAL) Our key observation is that, by incorporating auxiliary variables that mediate the effect of actions on system dynamics, it is sufficient to learn a lower bound of the mediator distribution function, instead of the Q-function. We provide theoretical guarantees for the algorithms we propose, and demonstrate their efficacy through simulations, as well as real-world experiments utilizing offline datasets from a leading ride-hailing platform.
  arXiv  Detail & Related papers  (2024-03-18T14:51:19Z)
• 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)
• Online Tensor Inference [0.0]
  Traditional offline learning, involving the storage and utilization of all data in each computational iteration, becomes impractical for high-dimensional tensor data. Existing low-rank tensor methods lack the capability for statistical inference in an online fashion. Our approach employs Gradient Descent (SGD) to enable efficient real-time data processing without extensive memory requirements.
  arXiv  Detail & Related papers  (2023-12-28T16:37:48Z)
• 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)
• Online learning in bandits with predicted context [8.257280652461159]
  We consider the contextual bandit problem where at each time, the agent only has access to a noisy version of the context. This setting is motivated by a wide range of applications where the true context for decision-making is unobserved. We propose the first online algorithm in this setting with sublinear regret guarantees under mild conditions.
  arXiv  Detail & Related papers  (2023-07-26T02:33:54Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• Dynamic Selection in Algorithmic Decision-making [9.172670955429906]
  This paper identifies and addresses dynamic selection problems in online learning algorithms with endogenous data. A novel bias (self-fulfilling bias) arises because the endogeneity of the data influences the choices of decisions. We propose an instrumental-variable-based algorithm to correct for the bias.
  arXiv  Detail & Related papers  (2021-08-28T01:41:37Z)
• The Interplay Between Implicit Bias and Benign Overfitting in Two-Layer Linear Networks [51.1848572349154]
  neural network models that perfectly fit noisy data can generalize well to unseen test data. We consider interpolating two-layer linear neural networks trained with gradient flow on the squared loss and derive bounds on the excess risk.
  arXiv  Detail & Related papers  (2021-08-25T22:01:01Z)
• Near-optimal inference in adaptive linear regression [60.08422051718195]
  Even simple methods like least squares can exhibit non-normal behavior when data is collected in an adaptive manner. We propose a family of online debiasing estimators to correct these distributional anomalies in at least squares estimation. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.
  arXiv  Detail & Related papers  (2021-07-05T21:05:11Z)
• Efficient First-Order Contextual Bandits: Prediction, Allocation, and Triangular Discrimination [82.52105963476703]
  A recurring theme in statistical learning, online learning, and beyond is that faster convergence rates are possible for problems with low noise. First-order guarantees are relatively well understood in statistical and online learning. We show that the logarithmic loss and an information-theoretic quantity called the triangular discrimination play a fundamental role in obtaining first-order guarantees.
  arXiv  Detail & Related papers  (2021-07-05T19:20:34Z)
• Post-Contextual-Bandit Inference [57.88785630755165]
  Contextual bandit algorithms are increasingly replacing non-adaptive A/B tests in e-commerce, healthcare, and policymaking. They can both improve outcomes for study participants and increase the chance of identifying good or even best policies. To support credible inference on novel interventions at the end of the study, we still want to construct valid confidence intervals on average treatment effects, subgroup effects, or value of new policies.
  arXiv  Detail & Related papers  (2021-06-01T12:01:51Z)
• Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems [1.6709415233613623]
  This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of distributional system uncertainty via a parameterized, control-dependent ambiguity set. We also introduce an online version of Nesterov's accelerated-gradient algorithm, and analyze its performance to solve this class of problems via dissipativity theory.
  arXiv  Detail & Related papers  (2021-02-18T01:49:06Z)
• Statistical Inference for Online Decision Making via Stochastic Gradient Descent [31.103438051597887]
  We propose an online algorithm that can make decisions and update the decision rule online via gradient descent. It is not only efficient but also supports all kinds of parametric reward models. The proposed algorithm and theoretical results are tested by simulations and a real data application to news article recommendation.
  arXiv  Detail & Related papers  (2020-10-14T18:25:18Z)
• Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination [29.85468294601847]
  We revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits. We show that our algorithms succeed where conventional methods fail.
  arXiv  Detail & Related papers  (2020-10-08T17:59:05Z)
• Learning while Respecting Privacy and Robustness to Distributional Uncertainties and Adversarial Data [66.78671826743884]
  The distributionally robust optimization framework is considered for training a parametric model. The objective is to endow the trained model with robustness against adversarially manipulated input data. Proposed algorithms offer robustness with little overhead.
  arXiv  Detail & Related papers  (2020-07-07T18:25:25Z)
• Dynamic Federated Learning [57.14673504239551]
  Federated learning has emerged as an umbrella term for centralized coordination strategies in multi-agent environments. We consider a federated learning model where at every iteration, a random subset of available agents perform local updates based on their data. Under a non-stationary random walk model on the true minimizer for the aggregate optimization problem, we establish that the performance of the architecture is determined by three factors, namely, the data variability at each agent, the model variability across all agents, and a tracking term that is inversely proportional to the learning rate of the algorithm.
  arXiv  Detail & Related papers  (2020-02-20T15:00:54Z)

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.