Expected Utility Networks

We introduce a new class of graphical representations, expected utility networks (EUNs), and discuss some of its properties and potential applications to artificial intelligence and economic theory. In EUNs not only probabilities, but also utilities enjoy a modular representation. EUNs are undirected graphs with two types of arc, representing probability and utility dependencies respectively. The representation of utilities is based on a novel notion of conditional utility independence, which we introduce and discuss in the context of other existing proposals. Just as probabilistic inference involves the computation of conditional probabilities, strategic inference involves the computation of conditional expected utilities for alternative plans of action. We define a new notion of conditional expected utility (EU) independence, and show that in EUNs node separation with respect to the probability and utility subgraphs implies conditional EU independence.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Directed expected utility networks

A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, such as, for example, conditional utility independence and generalized additive independence, have more recently started to appear. In this paper, we define a new graphical model, called a directed expected utility network, whose edges depict both probabilistic and utility conditional independences. These embed a very flexible class of utility models, much larger than those usually conceived in standard influence diagrams. Our graphical representation and various transformations of the original graph into a tree structure are then used to guide fast routines for the computation of a decision problem’s expected utilities. We show that our routines generalize those usually utilized in standard influence diagrams’ evaluations under much more restrictive conditions. We then proceed with the construction of a directed expected utility network to support decision makers in the domain of household food security

Risk measures on networks and expected utility

In reliability theory projects are usually evaluated in terms of their riskiness, and often decision under risk is intended as the one-shot-type binary choice of accepting or not accepting the risk. In this paper we elaborate on the concept of risk acceptance, and propose a theoretical framework based on network theory. In doing this, we deal with system reliability, where the interconnections among the random quantities involved in the decision process are explicitly taken into account. Furthermore, we explore the conditions to be satisfied for risk-acceptance criteria to be consistent with the axiomatization of standard expected utility theory within the network framework. In accordance with existing literature, we show that a risk evaluation criterion can be meaningful even if it is not consistent with the standard axiomatization of expected utility, once this is suitably reinterpreted in the light of networks. Finally, we provide some illustrative examples

Ranking structured documents using utility theory in the Bayesian network retrieval model

In this paper a new method based on Utility and Decision theory is presented to deal with structured documents. The aim of the application of these methodologies is to refine a first ranking of structural units, generated by means of an Information Retrieval Model based on Bayesian Networks. Units are newly arranged in the new ranking by combining their posterior probabilities, obtained in the first stage, with the expected utility of retrieving them. The experimental work has been developed using the Shakespeare structured collection and the results show an improvement of the effectiveness of this new approach

Introducing Quantum-Like Influence Diagrams for Violations of the Sure Thing Principle

It is the focus of this work to extend and study the previously proposed quantum-like Bayesian networks to deal with decision-making scenarios by incorporating the notion of maximum expected utility in influence diagrams. The general idea is to take advantage of the quantum interference terms produced in the quantum-like Bayesian Network to influence the probabilities used to compute the expected utility of some action. This way, we are not proposing a new type of expected utility hypothesis. On the contrary, we are keeping it under its classical definition. We are only incorporating it as an extension of a probabilistic graphical model in a compact graphical representation called an influence diagram in which the utility function depends on the probabilistic influences of the quantum-like Bayesian network. Our findings suggest that the proposed quantum-like influence digram can indeed take advantage of the quantum interference effects of quantum-like Bayesian Networks to maximise the utility of a cooperative behaviour in detriment of a fully rational defect behaviour under the prisoner's dilemma game

Distributed Stochastic Nonconvex Optimization and Learning based on Successive Convex Approximation

We study distributed stochastic nonconvex optimization in multi-agent networks. We introduce a novel algorithmic framework for the distributed minimization of the sum of the expected value of a smooth (possibly nonconvex) function (the agents' sum-utility) plus a convex (possibly nonsmooth) regularizer. The proposed method hinges on successive convex approximation (SCA) techniques, leveraging dynamic consensus as a mechanism to track the average gradient among the agents, and recursive averaging to recover the expected gradient of the sum-utility function. Almost sure convergence to (stationary) solutions of the nonconvex problem is established. Finally, the method is applied to distributed stochastic training of neural networks. Numerical results confirm the theoretical claims, and illustrate the advantages of the proposed method with respect to other methods available in the literature.Comment: Proceedings of 2019 Asilomar Conference on Signals, Systems, and Computer

Lightning Creation Games

Payment channel networks (PCNs) are a promising solution to the scalability problem of cryptocurrencies. Any two users connected by a payment channel in the network can theoretically send an unbounded number of instant, costless transactions between them. Users who are not directly connected can also transact with each other in a multi-hop fashion. In this work, we study the incentive structure behind the creation of payment channel networks, particularly from the point of view of a single user that wants to join the network. We define a utility function for a new user in terms of expected revenue, expected fees, and the cost of creating channels, and then provide constant factor approximation algorithms that optimise the utility function given a certain budget. Additionally, we take a step back from a single user to the whole network and examine the parameter spaces under which simple graph topologies form a Nash equilibrium

The Welfare Effects of Restricted Hospital Choice in the US Medical Care Market

Managed care health insurers in the US restrict their enrollees' choice of hospitals to within specific networks. This paper considers the implications of these restrictions. A three-step econometric model is used to predict consumer preferences over health plans conditional on the hospitals they offer. The results indicate that consumers place a positive and significant weight on their expected utility from the hospital network when choosing plans. A welfare analysis, assuming fixed prices, implies that restricting consumers' choice of hospitals leads to a loss to society of approximately $1 billion per year across the 43 US markets considered. This figure may be outweighed by the price reductions generated by the restriction.