Sequential Decision Making on Unmatched Data using Bayesian Kernel Embeddings

• URL: http://arxiv.org/abs/2210.13692v1
• Date: Tue, 25 Oct 2022 01:27:29 GMT
• Title: Sequential Decision Making on Unmatched Data using Bayesian Kernel Embeddings
• Authors: Diego Martinez-Taboada, Dino Sejdinovic
• Abstract summary: We propose a novel algorithm for maximizing the expectation of a function. We take into consideration the uncertainty derived from the estimation of both the conditional distribution of the features and the unknown function. Our algorithm empirically outperforms the current state-of-the-art algorithm in the experiments conducted.
• Score: 10.75801980090826
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given context and an action taken by an agent. In contrast to Bayesian optimization, the arguments of the function are not under agent's control, but are indirectly determined by the agent's action based on a given context. If the information of the features is to be included in the maximization problem, the full conditional distribution of such features, rather than its expectation only, needs to be accounted for. Furthermore, the function is itself unknown, only counting with noisy observations of such function, and potentially requiring the use of unmatched data sets. We propose a novel algorithm for the aforementioned problem which takes into consideration the uncertainty derived from the estimation of both the conditional distribution of the features and the unknown function, by modeling the former as a Bayesian conditional mean embedding and the latter as a Gaussian process. Our algorithm empirically outperforms the current state-of-the-art algorithm in the experiments conducted.

Related papers

• Uncertainty Quantification with Bayesian Higher Order ReLU KANs [0.0]
  We introduce the first method of uncertainty quantification in the domain of Kolmogorov-Arnold Networks, specifically focusing on (Higher Order) ReLUKANs. We validate our method through a series of closure tests, including simple one-dimensional functions. We demonstrate the method's ability to correctly identify functional dependencies introduced through the inclusion of a term.
  arXiv  Detail & Related papers  (2024-10-02T15:57:18Z)
• Information-Theoretic Safe Bayesian Optimization [59.758009422067005]
  We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an unknown (safety) constraint. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. We propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate.
  arXiv  Detail & Related papers  (2024-02-23T14:31:10Z)
• Robust Non-parametric Knowledge-based Diffusion Least Mean Squares over Adaptive Networks [12.266804067030455]
  The proposed algorithm leads to a robust estimation of an unknown parameter vector in a group of cooperative estimators. Results show the robustness of the proposed algorithm in the presence of different noise types.
  arXiv  Detail & Related papers  (2023-12-03T06:18:59Z)
• Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization [73.80101701431103]
  The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. We study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility.
  arXiv  Detail & Related papers  (2023-04-17T14:23:43Z)
• Generalizing Bayesian Optimization with Decision-theoretic Entropies [102.82152945324381]
  We consider a generalization of Shannon entropy from work in statistical decision theory. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures. We then show how alternative choices for the loss yield a flexible family of acquisition functions.
  arXiv  Detail & Related papers  (2022-10-04T04:43:58Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Inference on Strongly Identified Functionals of Weakly Identified Functions [71.42652863687117]
  We study a novel condition for the functional to be strongly identified even when the nuisance function is not. We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
  arXiv  Detail & Related papers  (2022-08-17T13:38:31Z)
• Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals [16.768606469968113]
  We consider a class of doubly robust moment functions originally introduced in (Robins et al., 2008) We demonstrate that this moment function can be used to construct estimating equations for the nuisance functions. The convergence rates of the nuisance functions are analyzed using the modern techniques in statistical learning theory.
  arXiv  Detail & Related papers  (2021-04-07T05:52:15Z)
• Oblivious Data for Fairness with Kernels [1.599072005190786]
  We investigate the problem of algorithmic fairness in the case where sensitive and non-sensitive features are available. Our key ingredient for generating such oblivious features is a Hilbert-space-valued conditional expectation. We propose a plug-in approach and demonstrate how the estimation errors can be controlled.
  arXiv  Detail & Related papers  (2020-02-07T16:59:24Z)
• Options of Interest: Temporal Abstraction with Interest Functions [58.30081828754683]
  We provide a generalization of initiation sets suitable for general function approximation, by defining an interest function associated with an option. We derive a gradient-based learning algorithm for interest functions, leading to a new interest-option-critic architecture.
  arXiv  Detail & Related papers  (2020-01-01T21:24:39Z)

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.