17,798 research outputs found
Optimal discovery with probabilistic expert advice
peer reviewedMotivated by issues of security analysis for power systems, we analyze a new problem, called optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and the Good-Turingmissing mass estimator. We show that this strategy attains the optimal discovery rate in a macroscopic limit sense, under some assumptions on the probabilistic experts. We also provide numerical experiments suggesting that this optimal behavior may still hold under weaker assumptions
Optimality of Universal Bayesian Sequence Prediction for General Loss and Alphabet
Various optimality properties of universal sequence predictors based on
Bayes-mixtures in general, and Solomonoff's prediction scheme in particular,
will be studied. The probability of observing at time , given past
observations can be computed with the chain rule if the true
generating distribution of the sequences is known. If
is unknown, but known to belong to a countable or continuous class \M
one can base ones prediction on the Bayes-mixture defined as a
-weighted sum or integral of distributions \nu\in\M. The cumulative
expected loss of the Bayes-optimal universal prediction scheme based on
is shown to be close to the loss of the Bayes-optimal, but infeasible
prediction scheme based on . We show that the bounds are tight and that no
other predictor can lead to significantly smaller bounds. Furthermore, for
various performance measures, we show Pareto-optimality of and give an
Occam's razor argument that the choice for the weights
is optimal, where is the length of the shortest program describing
. The results are applied to games of chance, defined as a sequence of
bets, observations, and rewards. The prediction schemes (and bounds) are
compared to the popular predictors based on expert advice. Extensions to
infinite alphabets, partial, delayed and probabilistic prediction,
classification, and more active systems are briefly discussed.Comment: 34 page
Bell nonlocality and Bayesian game theory
We discuss a connection between Bell nonlocality and Bayesian games. This
link offers interesting perspectives for Bayesian games, namely to allow the
players to receive advice in the form of nonlocal correlations, for instance
using entangled quantum particles or more general no-signaling boxes. The
possibility of having such 'nonlocal advice' will lead to novel joint
strategies, impossible to achieve in the classical setting. This implies that
quantum resources, or more general no-signaling resources, offer a genuine
advantage over classical ones. Moreover, some of these strategies can represent
equilibrium points, leading to the notion of quantum/no-signaling Nash
equilibrium. Finally we describe new types of question in the study of
nonlocality, namely the consideration of non-local advantage when there is a
set of Bell expressions.Comment: 7 pages, 3 figure
Structuring Decisions Under Deep Uncertainty
Innovative research on decision making under ‘deep uncertainty’ is underway in applied fields such as engineering and operational research, largely outside the view of normative theorists grounded in decision theory. Applied methods and tools for decision support under deep uncertainty go beyond standard decision theory in the attention that they give to the structuring of decisions. Decision structuring is an important part of a broader philosophy of managing uncertainty in decision making, and normative decision theorists can both learn from, and contribute to, the growing deep uncertainty decision support literature
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