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The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric…

We resolve the complexity of revenue-optimal deterministic auctions in the unit-demand single-buyer Bayesian setting, i.e., the optimal item pricing problem, when the buyer's values for the items are independent. We show that the problem of…

We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…

Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…

This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…

We consider the problem of computing the value and an optimal strategy for minimizing the expected termination time in one-counter Markov decision processes. Since the value may be irrational and an optimal strategy may be rather…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

We propose an improved method for estimating partial differential equations and delay partial differential equations from data, using Bayesian optimization and the Bayesian information criterion to automatically find suitable…

Bayesian Optimization is an effective method for searching the global maxima of an objective function especially if the function is unknown. The process comprises of using a surrogate function and choosing an acquisition function followed…

We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…

Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…

Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…

We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…

The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…

We review typical design problems encountered in the planning of observational studies and propose a unifying framework that allows us to use the same concepts and notation for different problems. In the framework, the design is defined as…

The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed…