In this document, Section 1 contains some lemmas used in subsequent proofs, Section 2 presents an extended proof of the bound on the domain disagreement disρ(DS , DT ) (Theorem 3 of the main paper), Section 3 introduces other PAC-Bayesian bounds for disρ(DS , DT ) and RPT (Gρ), Section 4 shows equations and implementation details about PBDA (our proposed learning algorithm for PAC-Bayesian DA t...

We establish the existence of perfect Bayesian equilibria in general menu games, known to be sufficient to analyze common agency problems. Our main result states that every menu game satisfying enough continuity properties has a perfect Bayesian equilibrium. Despite the continuity assumptions that we make, discontinuities naturally arise due to the absence, in general, of continuous optimal cho...

We introduce a simple, general framework for likelihood-free Bayesian reinforcement learning, through Approximate Bayesian Computation (ABC). The advantage is that we only require a prior distribution on a class of simulators. This is useful when a probabilistic model of the underlying process is too complex to formulate, but where detailed simulation models are available. ABC-RL allows the use...

“Damned by Faint Praise” is the phenomenon whereby weak positive information leads to a negative change in belief. However, in a Bayesian model of belief revision positive information can seemingly only exert a positive change in belief. We introduce a version of Bayes’ Theorem incorporating the concept of epistemic closure. This reformalization is able to predict the conditions under which a ‘...

We investigate sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem (CJT ). In the Bayesian game Gn among n jurors, we allow for arbitrary distribution on the types of jurors. In particular, any kind of dependency is possible. If each juror i has a “constant strategy”, σ i (that is, a strategy that is independent of the size n≥ i of the jur...

Bayesian analysis provides a normative framework for use of uncertain information in decision making and inference. From a practical perspective, Bayes Theorem has a logical appeal in that it characterizes a process of knowledge updating that is based on pooling precision-weighted information. For years however, Bayesian inference was largely ignored or even discredited in favor of frequentist ...

The asymptotic minimax theorem for Bernoully twoarmed bandit problem states that the minimax risk has the order N as N → ∞, where N is the control horizon, and provides lower and upper estimates. It can be easily extended to normal two-armed bandit. For normal two-armed bandit, we generalize the asymptotic minimax theorem as follows: the minimax risk is approximately equal to 0.637N as N →∞. Ke...

Approximate Bayesian Gaussian process (GP) classification techniques are powerful nonparametric learning methods, similar in appearance and performance to Support Vector machines. Based on simple probabilistic models, they render interpretable results and can be embedded in Bayesian frameworks for model selection, feature selection, etc. In this paper, by applying the PAC-Bayesian theorem of nc...