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We study Gaussian Process Thompson Sampling (GP-TS) for sequential decision-making over compact, continuous action spaces and provide a frequentist regret analysis based on fractional Gaussian process posteriors, without relying on domain…
We address online combinatorial optimization when the player has a prior over the adversary's sequence of losses. In this framework, Russo and Van Roy proposed an information-theoretic analysis of Thompson Sampling based on the information…
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 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 empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently…
Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a…
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better…
We consider a linear stochastic bandit problem where the dimension $K$ of the unknown parameter $\theta$ is larger than the sampling budget $n$. In such cases, it is in general impossible to derive sub-linear regret bounds since usual…
In a low-rank linear bandit problem, the reward of an action (represented by a matrix of size $d_1 \times d_2$) is the inner product between the action and an unknown low-rank matrix $\Theta^*$. We propose an algorithm based on a novel…
We consider the adversarial linear contextual bandit setting, which allows for the loss functions associated with each of $K$ arms to change over time without restriction. Assuming the $d$-dimensional contexts are drawn from a fixed known…
In this work, we close the fundamental gap of theory and practice by providing an improved regret bound for linear ensemble sampling. We prove that with an ensemble size logarithmic in $T$, linear ensemble sampling can achieve a frequentist…
Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds. When…
In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret,…
We study the performance of the Thompson Sampling algorithm for logistic bandit problems. In this setting, an agent receives binary rewards with probabilities determined by a logistic function, $\exp(\beta \langle a, \theta…
Generalized Linear Bandits (GLBs) are powerful extensions to the Linear Bandit (LB) setting, broadening the benefits of reward parametrization beyond linearity. In this paper we study GLBs in non-stationary environments, characterized by a…
We propose a linear contextual bandit algorithm with $O(\sqrt{dT\log T})$ regret bound, where $d$ is the dimension of contexts and $T$ isthe time horizon. Our proposed algorithm is equipped with a novel estimator in which exploration is…
Assuming distributions are Gaussian often facilitates computations that are otherwise intractable. We study the performance of an agent that attains a bounded information ratio with respect to a bandit environment with a Gaussian prior…
We study how representation learning can improve the efficiency of bandit problems. We study the setting where we play $T$ linear bandits with dimension $d$ concurrently, and these $T$ bandit tasks share a common $k (\ll d)$ dimensional…
Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems.…
We study dynamic regret minimization in unconstrained adversarial linear bandit problems. In this setting, a learner must minimize the cumulative loss relative to an arbitrary sequence of comparators…