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Decision theory has become widely accepted in the AI community as a useful framework for planning and decision making. Applying the framework typically requires elicitation of some form of probability and utility information. While much…

We present a modular approach to reinforcement learning that uses a Bayesian representation of the uncertainty over models. The approach, BOSS (Best of Sampled Set), drives exploration by sampling multiple models from the posterior and…

The exploration-exploitation dilemma has been an intriguing and unsolved problem within the framework of reinforcement learning. "Optimism in the face of uncertainty" and model building play central roles in advanced exploration methods.…

Spline basis exploration via Bayesian model selection is a widely employed strategy for determining the optimal set of basis terms in nonparametric regression. However, despite its widespread use, this approach often encounters performance…

Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…

We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $\alpha$-H\"older continuous (including Lipschitz) functions with $0<\alpha\leq 1$. Our main…

Bayesian Optimization is a widely used method for optimizing expensive black-box functions, relying on probabilistic surrogate models such as Gaussian Processes. The quality of the surrogate model is crucial for good optimization…

Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven success in applications for decades, important open questions remain on the theoretical convergence behaviors…

Data-driven algorithm design, that is, choosing the best algorithm for a specific application, is a crucial problem in modern data science. Practitioners often optimize over a parameterized algorithm family, tuning parameters based on…

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes,…

Bayesian optimization (BO) is a popular algorithm for solving challenging optimization tasks. It is designed for problems where the objective function is expensive to evaluate, perhaps not available in exact form, without gradient…

In this work, we address the challenge of data-efficient exploration in reinforcement learning by examining existing principled, information-theoretic approaches to intrinsic motivation. Specifically, we focus on a class of exploration…

Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and…

We consider a multi-objective optimization problem with objective functions that are expensive to evaluate. The decision maker (DM) has unknown preferences, and so the standard approach is to generate an approximation of the Pareto front…

Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function…

We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on…

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…

Domain experts often possess valuable physical insights that are overlooked in fully automated decision-making processes such as Bayesian optimisation. In this article we apply high-throughput (batch) Bayesian optimisation alongside…

Bayesian Optimization, leveraging Gaussian process models, has proven to be a powerful tool for minimizing expensive-to-evaluate objective functions by efficiently exploring the search space. Extensions such as constrained Bayesian…

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…