Coherent and Archimedean choice in general Banach spaces

• URL: http://arxiv.org/abs/2002.05461v4
• Date: Fri, 9 Jul 2021 13:03:31 GMT
• Title: Coherent and Archimedean choice in general Banach spaces
• Authors: Gert de Cooman
• Abstract summary: I introduce and study a new notion of Archimedeanity for binary and non-binary choice between options that live in an abstract Banach space. The representation theorems proved here provide an axiomatic characterisation for, amongst many other choice methods, Levi's E-admissibility and Walley-Sen maximality.
• Score: 0.45687771576879593
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: I introduce and study a new notion of Archimedeanity for binary and non-binary choice between options that live in an abstract Banach space, through a very general class of choice models, called sets of desirable option sets. In order to be able to bring an important diversity of contexts into the fold, amongst which choice between horse lottery options, I pay special attention to the case where these linear spaces don't include all `constant' options.I consider the frameworks of conservative inference associated with Archimedean (and coherent) choice models, and also pay quite a lot of attention to representation of general (non-binary) choice models in terms of the simpler, binary ones.The representation theorems proved here provide an axiomatic characterisation for, amongst many other choice methods, Levi's E-admissibility and Walley-Sen maximality.

Related papers

• Differentiating Choices via Commonality for Multiple-Choice Question Answering [54.04315943420376]
  Multiple-choice question answering can provide valuable clues for choosing the right answer. Existing models often rank each choice separately, overlooking the context provided by other choices. We propose a novel model by differentiating choices through identifying and eliminating their commonality, called DCQA.
  arXiv  Detail & Related papers  (2024-08-21T12:05:21Z)
• A Canonicalization Perspective on Invariant and Equivariant Learning [54.44572887716977]
  We introduce a canonicalization perspective that provides an essential and complete view of the design of frames. We show that there exists an inherent connection between frames and canonical forms. We design novel frames for eigenvectors that are strictly superior to existing methods.
  arXiv  Detail & Related papers  (2024-05-28T17:22:15Z)
• Choosing on Sequences [0.0]
  We propose a new framework that considers choice from infinite sequences. We show that bounded attention is due to the continuity of the choice functions with respect to a natural topology. We introduce the notion of computability of a choice function using Turing machines and show that computable choice rules can be implemented by a finite automaton.
  arXiv  Detail & Related papers  (2022-02-28T20:16:24Z)
• Robust SVM Optimization in Banach spaces [0.0]
  We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach spaces. These include the Representer Theorem, strong duality for the associated Optimization problem as well as their geometric interpretation.
  arXiv  Detail & Related papers  (2022-02-17T10:32:06Z)
• Universal and data-adaptive algorithms for model selection in linear contextual bandits [52.47796554359261]
  We consider the simplest non-trivial instance of model-selection: distinguishing a simple multi-armed bandit problem from a linear contextual bandit problem. We introduce new algorithms that explore in a data-adaptive manner and provide guarantees of the form $mathcalO(dalpha T1- alpha)$. Our approach extends to model selection among nested linear contextual bandits under some additional assumptions.
  arXiv  Detail & Related papers  (2021-11-08T18:05:35Z)
• Choice functions based multi-objective Bayesian optimisation [1.0742675209112622]
  We introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning.
  arXiv  Detail & Related papers  (2021-10-15T17:24:03Z)
• Temporal Abstraction in Reinforcement Learning with the Successor Representation [65.69658154078007]
  We argue that the successor representation (SR) can be seen as a natural substrate for the discovery and use of temporal abstractions. We show how the SR can be used to discover options that facilitate either temporally-extended exploration or planning.
  arXiv  Detail & Related papers  (2021-10-12T05:07:43Z)
• Preference learning along multiple criteria: A game-theoretic perspective [97.94912276610002]
  We generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization. We show that the Blackwell winner of a multi-criteria problem instance can be computed as the solution to a convex optimization problem.
  arXiv  Detail & Related papers  (2021-05-05T03:23:11Z)
• Switch Spaces: Learning Product Spaces with Sparse Gating [48.591045282317424]
  We propose Switch Spaces, a data-driven approach for learning representations in product space. We introduce sparse gating mechanisms that learn to choose, combine and switch spaces. Experiments on knowledge graph completion and item recommendations show that the proposed switch space achieves new state-of-the-art performances.
  arXiv  Detail & Related papers  (2021-02-17T11:06:59Z)
• Inference with Choice Functions Made Practical [1.1859913430860332]
  We study how to infer new choices from previous choices in a conservative manner. We use the theory of choice functions: a unifying mathematical framework for conservative decision making.
  arXiv  Detail & Related papers  (2020-05-07T12:58:05Z)

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.