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

Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear…

This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase, and we design an adaptive experiment…

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected…

Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or…

Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We…

This paper focuses on finite-player incomplete information games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolutely…

We investigate a two-period Bayesian persuasion game, where the receiver faces a decision, akin to a one-armed bandit problem: to undertake an action, gaining noisy information and a corresponding positive or negative payoff, or to refrain.…

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

Two fundamental problems in computational game theory are computing a Nash equilibrium and learning to exploit opponents given observations of their play (opponent exploitation). The latter is perhaps even more important than the former:…

Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we…

We investigate the problem of continuous-time causal estimation under a minimax criterion. Let $X^T = \{X_t,0\leq t\leq T\}$ be governed by the probability law $P_{\theta}$ from a class of possible laws indexed by $\theta \in \Lambda$, and…

We study online Bayesian persuasion problems in which an informed sender repeatedly faces a receiver with the goal of influencing their behavior through the provision of payoff-relevant information. Previous works assume that the sender has…

We show that it can be suboptimal for Bayesian decision-making agents employing social learning to use correct prior probabilities as their initial beliefs. We consider sequential Bayesian binary hypothesis testing where each individual…

We introduce and study the problem of detecting whether an agent is updating their prior beliefs given new evidence in an optimal way that is Bayesian, or whether they are biased towards their own prior. In our model, biased agents form…

Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of…

Many multi-agent interaction scenarios can be naturally modeled as noncooperative games, where each agent's decisions depend on others' future actions. However, deploying game-theoretic planners for autonomous decision-making requires a…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…