相关论文: On the Suboptimality of GP-UCB under Polynomial Ef…

In this paper, the problem of maximizing a black-box function $f:\mathcal{X} \to \mathbb{R}$ is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high…

We propose a novel variant of the UCB algorithm (referred to as Efficient-UCB-Variance (EUCBV)) for minimizing cumulative regret in the stochastic multi-armed bandit (MAB) setting. EUCBV incorporates the arm elimination strategy proposed in…

We consider the problem of optimizing a black-box function based on noisy bandit feedback. Kernelized bandit algorithms have shown strong empirical and theoretical performance for this problem. They heavily rely on the assumption that the…

We consider optimizing a function network in the noise-free grey-box setting with RKHS function classes, where the exact intermediate results are observable. We assume that the structure of the network is known (but not the underlying…

In this paper, we consider algorithm-independent lower bounds for the problem of black-box optimization of functions having a bounded norm is some Reproducing Kernel Hilbert Space (RKHS), which can be viewed as a non-Bayesian Gaussian…

We consider black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes…

Bayesian optimization (BO) is a widely used iterative algorithm for optimizing black-box functions. Each iteration requires maximizing an acquisition function, such as the upper confidence bound (UCB) or a sample path from the Gaussian…

The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his…

We consider the stochastic bandit problem with a continuous set of arms, with the expected reward function over the arms assumed to be fixed but unknown. We provide two new Gaussian process-based algorithms for continuous bandit…

In this paper, we consider the problem of sequentially optimizing a black-box function $f$ based on noisy samples and bandit feedback. We assume that $f$ is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert…

We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box…

We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function $f^*$ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by…

In this paper, we consider the time-varying Bayesian optimization problem. The unknown function at each time is assumed to lie in an RKHS (reproducing kernel Hilbert space) with a bounded norm. We adopt the general variation budget model to…

Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration…

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…

Confidence bounds are an essential tool for rigorously quantifying the uncertainty of predictions. They are a core component in many sequential learning and decision-making algorithms, with tighter confidence bounds giving rise to…

I present the first algorithm for stochastic finite-armed bandits that simultaneously enjoys order-optimal problem-dependent regret and worst-case regret. Besides the theoretical results, the new algorithm is simple, efficient and…

One of the key drivers of complexity in the classical (stochastic) multi-armed bandit (MAB) problem is the difference between mean rewards in the top two arms, also known as the instance gap. The celebrated Upper Confidence Bound (UCB)…

We study an algorithm-independent, worst-case lower bound for the Gaussian process (GP) bandit problem in the frequentist setting, where the reward function is fixed and has a bounded norm in the known reproducing kernel Hilbert space…

The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly…