Minimality and comparison of sets of multi-attribute vectors

Toffano, Federico; Wilson, Nic

doi:10.1007/s10458-022-09572-8

Cited by 4 publications

(4 citation statements)

References 53 publications

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“…We can compute PO(A, W) with a linear programming solver (see, e.g., [20]). Briefly, we can test if α ∈ PO(A, W) evaluating the feasibility of the set of linear constraints u(α, w) ≥ u(β, w) for all β ∈ A \ {α} with w ∈ W. We focus only on the alternatives in PO(A, W) because the decision-maker's most preferred alternative must be optimal for the true preference w * .…”

Section: Problem Settingmentioning

confidence: 99%

An Efficient Non-Bayesian Approach for Interactive Preference Elicitation Under Noisy Preference Models

Pourkhajouei,

Toffano,

Viappiani

et al. 2023

Lecture Notes in Computer Science

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The development of models that can cope with noisy input preferences is a critical topic in artificial intelligence methods for interactive preference elicitation. A Bayesian representation of the uncertainty in the user preference model can be used to successfully handle this, but there are large costs in terms of the processing time required to update the probabilistic model upon receiving the user's answers, to compute the optimal recommendation and to select the next queries to ask; these costs limit the adoption of these techniques in real-time contexts. A Bayesian approach also requires one to assume a prior distribution over the set of user preference models. In this work, dealing with multi-criteria decision problems, we consider instead a more qualitative approach to preference uncertainty, focusing on the most plausible user preference models, and aim to generate a query strategy that enables us to find an alternative that is optimal in all of the most plausible preference models. We develop a non-Bayesian algorithmic method for recommendation and interactive elicitation that considers a large number of possible user models that are evaluated with respect to their degree of consistency of the input preferences. This suggests methods for generating queries that are reasonably fast to compute. Our test results demonstrate the viability of our approach, including in real-time contexts, with high accuracy in recommending the most preferred alternative for the user.

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Section: Problem Settingmentioning

confidence: 99%

An Efficient Non-Bayesian Approach for Interactive Preference Elicitation Under Noisy Preference Models

Pourkhajouei,

Toffano,

Viappiani

et al. 2023

Lecture Notes in Computer Science

Self Cite

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“…The max regret and minimax regret measures [18] have often been used for decision problems under uncertainty, as non-Bayesian methods for reasoning about an unknown user preference model; in particular, for recommending alternatives, in generating queries, and in deciding when to terminate the user interaction, see e.g., [23,3,5,12,1,22]. One natural way of computing max regret is using extreme points [19,20]. Weighted average and other linear preference models are a very commonly used special case of Multi-Attribute Utility Theory (MAUT) [16,11,7].…”

Section: Related Workmentioning

confidence: 99%

“…However, we might have used different units for the monetary gain, e.g., using cents rather than euros. The new representation α of α is equal to (20,200), and β = (44, 100) and δ = (24, 100), and thus λ = (−4, 100). The extreme points of W 1 Λ are u = (0, 1) and v = ( 25 26 , 1 26 ) leading to a max regret for α equalling…”

Section: Motivating Examplementioning

confidence: 99%

On the Variation of Max Regret with Respect to the Scaling of the Objectives

Wilson

2023

Frontiers in Artificial Intelligence and Applications

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In a multi-objective optimisation problem, when there is uncertainty regarding the correct user preference model, max regret is a natural measure for how far an alternative is from being necessarily optimal (i.e., optimal with respect to every candidate preference model). It can be used for recommending a relatively safe choice to the user, or used in the generation of an informative query, and in the decision to terminate the user interaction, because an alternative is sufficiently close to being necessarily optimal. We consider a common and simple form of user preference model: a weighted average over the objectives (with unknown weights). However, changing the scale of an objective by a linear factor leads to an essentially different set of preference models, and this changes the max regret values (and potentially their relative ordering), sometimes very considerably. Since the scaling of the objectives is often partly subjective and somewhat arbitrary, it is important to be aware of how sensitive the max regret values are to the choices of scaling of the objectives. We give mathematical results that characterise and enable computation of this variability, along with an asymptotic analysis.

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“…UD X is rationalizable, but PO X typically is not (because the Expansion property is not maintained by union). Therefore, non-rationalizable consistent Plott functions (PO X ) are important in preference elicitation methods, e.g., [12,3,4,21].…”

Section: Plott Functions Generated From Partial Informationmentioning

confidence: 99%

Enforcing Natural Properties of Choice Functions, with Application for Combination

Wilson

2023

Frontiers in Artificial Intelligence and Applications

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One important and natural representation of preferences is a choice function, which returns the preferred options amongst any given subset of the alternatives. There are some very intuitive coherence conditions that might be assumed for an agent’s choice function, in particular path independence, and a consistency condition stating that there is always at least one preferred alternative among any non-empty set. However, an elicited choice function may not satisfy path independence, because of the elicitation being incomplete, or because of there being some incoherence in the agent’s reported choice function (despite the agent assenting to the general coherence conditions). Furthermore, if we wish to combine the choice functions of more than one agent, simple natural combination operations can lose path independence. This paper develops methods for enforcing path independence and restoring consistency, thus, making the user preferences coherent; this method also leads to approaches for combining two choice functions, in order to suggest the most promising alternatives for a pair of agents.

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Minimality and comparison of sets of multi-attribute vectors

Cited by 4 publications

References 53 publications

An Efficient Non-Bayesian Approach for Interactive Preference Elicitation Under Noisy Preference Models

An Efficient Non-Bayesian Approach for Interactive Preference Elicitation Under Noisy Preference Models

On the Variation of Max Regret with Respect to the Scaling of the Objectives

Enforcing Natural Properties of Choice Functions, with Application for Combination

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