Related papers: Bayesimax Theory: Selecting Priors by Minimizing T…

This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…

In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective}…

When learning to play an imperfect information game, it is often easier to first start with the basic mechanics of the game rules. For example, one can play several example rounds with private cards revealed to all players to better…

In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…

Bayesian neural networks (BNNs) offer a natural probabilistic formulation for inference in deep learning models. Despite their popularity, their optimality has received limited attention through the lens of statistical decision theory. In…

What is the best way to exploit extra data -- be it unlabeled data from the same task, or labeled data from a related task -- to learn a given task? This paper formalizes the question using the theory of reference priors. Reference priors…

We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

The Markov Decision Process (MDP) is a popular framework for sequential decision-making problems, and uncertainty quantification is an essential component of it to learn optimal decision-making strategies. In particular, a Bayesian…

We study repeated two-player games where one of the players, the learner, employs a no-regret learning strategy, while the other, the optimizer, is a rational utility maximizer. We consider general Bayesian games, where the payoffs of both…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

This paper presents a decision-theoretic approach to statistical inference that satisfies the likelihood principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning…

This work is an application of game theory to quantum information. In a state estimate, we are given observations distributed according to an unknown distribution $P_{\theta}$ (associated with award $Q$), which Nature chooses at random from…

This paper considers Bayesian persuasion for routing games where information about the uncertain state of the network is provided by a traffic information system (TIS) using public signals. In this setup, the TIS commits to a signalling…

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…

Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is…

Classical reinforcement learning assumes the agent interacts with a fixed environment whose behavior does not depend on the agent's policy. This assumption breaks down in non-realizable settings where other actors might anticipate the…

Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from…