In this paper we introduce the pure exploration transductive linear bandit problem: given a set of measurement vectors $\mathcal{X}\subset \mathbb{R}^d$, a set of items $\mathcal{Z}\subset \mathbb{R}^d$, a fixed confidence $\delta$, and an unknown vector $\theta^{\ast}\in \mathbb{R}^d$, the goal is to infer $\arg\max_{z\in \mathcal{Z}} z^\top\theta^\ast$ with probability $1-\delta$ by making as few sequentially chosen noisy measurements of the form $x^\top\theta^{\ast}$ as possible. When $\mathcal{X}=\mathcal{Z}$, this setting generalizes linear bandits, and when $\mathcal{X}$ is the standard basis vectors and $\mathcal{Z}\subset \{0,1\}^d$, combinatorial bandits. The transductive setting naturally arises when the set of measurement vectors is limited due to factors such as availability or cost. As an example, in drug discovery the compounds and dosages $\mathcal{X}$ a practitioner may be willing to evaluate in the lab in vitro due to cost or safety reasons may differ vastly from those compounds and dosages $\mathcal{Z}$ that can be safely administered to patients in vivo. Alternatively, in recommender systems for books, the set of books $\mathcal{X}$ a user is queried about may be restricted to known best-sellers even though the goal might be to recommend more esoteric titles $\mathcal{Z}$. In this paper, we provide instance-dependent lower bounds for the transductive setting, an algorithm that matches these up to logarithmic factors, and an evaluation. In particular, we present the first non-asymptotic algorithm for linear bandits that nearly achieves the information-theoretic lower bound.

We propose a new adaptive sampling approach to multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (true positives). In addition, each distribution can be sequentially and repeatedly sampled. Using techniques from multi-armed bandits, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e.

In this paper we introduce the pure exploration transductive linear bandit problem: given a set of measurement vectors \mathcal{X}\subset \mathbb{R} d, a set of items \mathcal{Z}\subset \mathbb{R} d, a fixed confidence \delta, and an unknown vector \theta {\ast}\in \mathbb{R} d, the goal is to infer \arg\max_{z\in \mathcal{Z}} z \top\theta \ast with probability 1-\delta by making as few sequentially chosen noisy measurements of the form x \top\theta {\ast} as possible. The transductive setting naturally arises when the set of measurement vectors is limited due to factors such as availability or cost. As an example, in drug discovery the compounds and dosages \mathcal{X} a practitioner may be willing to evaluate in the lab in vitro due to cost or safety reasons may differ vastly from those compounds and dosages \mathcal{Z} that can be safely administered to patients in vivo. Alternatively, in recommender systems for books, the set of books \mathcal{X} a user is queried about may be restricted to known best-sellers even though the goal might be to recommend more esoteric titles \mathcal{Z} . In this paper, we provide instance-dependent lower bounds for the transductive setting, an algorithm that matches these up to logarithmic factors, and an evaluation.

In this study, we demonstrate a sequential experimental design for spectral measurements by active learning using parametric models as predictors. In spectral measurements, it is necessary to reduce the measurement time because of sample fragility and high energy costs. To improve the efficiency of experiments, sequential experimental designs are proposed, in which the subsequent measurement is designed by active learning using the data obtained before the measurement. Conventionally, parametric models are employed in data analysis; when employed for active learning, they are expected to afford a sequential experimental design that improves the accuracy of data analysis. However, due to the complexity of the formulas, a sequential experimental design using general parametric models has not been realized. Therefore, we applied Bayesian inference-based data analysis using the exchange Monte Carlo method to realize a sequential experimental design with general parametric models. In this study, we evaluated the effectiveness of the proposed method by applying it to Bayesian spectral deconvolution and Bayesian Hamiltonian selection in X-ray photoelectron spectroscopy. Using numerical experiments with artificial data, we demonstrated that the proposed method improves the accuracy of model selection and parameter estimation while reducing the measurement time compared with the results achieved without active learning or with active learning using the Gaussian process regression.

We consider the problem of counterfactual inference in sequentially designed experiments wherein a collection of $\mathbf{N}$ units each undergo a sequence of interventions for $\mathbf{T}$ time periods, based on policies that sequentially adapt over time. Our goal is counterfactual inference, i.e., estimate what would have happened if alternate policies were used, a problem that is inherently challenging due to the heterogeneity in the outcomes across units and time. To tackle this task, we introduce a suitable latent factor model where the potential outcomes are determined by exogenous unit and time level latent factors. Under suitable conditions, we show that it is possible to estimate the missing (potential) outcomes using a simple variant of nearest neighbors. First, assuming a bilinear latent factor model and allowing for an arbitrary adaptive sampling policy, we establish a distribution-free non-asymptotic guarantee for estimating the missing outcome of any unit at any time; under suitable regularity condition, this guarantee implies that our estimator is consistent. Second, for a generic non-parametric latent factor model, we establish that the estimate for the missing outcome of any unit at time $\mathbf{T}$ satisfies a central limit theorem as $\mathbf{T} \to \infty$, under suitable regularity conditions. Finally, en route to establishing this central limit theorem, we establish a non-asymptotic mean-squared-error bound for the estimate of the missing outcome of any unit at time $\mathbf{T}$. Our work extends the recently growing literature on inference with adaptively collected data by allowing for policies that pool across units, and also compliments the matrix completion literature when the entries are revealed sequentially in an arbitrarily dependent manner based on prior observed data.

In this paper we introduce the pure exploration transductive linear bandit problem: given a set of measurement vectors $\mathcal{X}\subset \mathbb{R} d$, a set of items $\mathcal{Z}\subset \mathbb{R} d$, a fixed confidence $\delta$, and an unknown vector $\theta {\ast}\in \mathbb{R} d$, the goal is to infer $\arg\max_{z\in \mathcal{Z}} z \top\theta \ast$ with probability $1-\delta$ by making as few sequentially chosen noisy measurements of the form $x \top\theta {\ast}$ as possible. When $\mathcal{X} \mathcal{Z}$, this setting generalizes linear bandits, and when $\mathcal{X}$ is the standard basis vectors and $\mathcal{Z}\subset \{0,1\} d$, combinatorial bandits. The transductive setting naturally arises when the set of measurement vectors is limited due to factors such as availability or cost. As an example, in drug discovery the compounds and dosages $\mathcal{X}$ a practitioner may be willing to evaluate in the lab in vitro due to cost or safety reasons may differ vastly from those compounds and dosages $\mathcal{Z}$ that can be safely administered to patients in vivo. Alternatively, in recommender systems for books, the set of books $\mathcal{X}$ a user is queried about may be restricted to known best-sellers even though the goal might be to recommend more esoteric titles $\mathcal{Z}$.

We propose a new adaptive sampling approach to multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (true positives). In addition, each distribution can be sequentially and repeatedly sampled. Using techniques from multi-armed bandits, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e. Our sample complexity results match known information theoretic lower bounds and through simulations we show a substantial performance improvement over uniform sampling and an adaptive elimination style algorithm.

The spectral energy distribution (SED) is a relatively easy way for astronomers to distinguish between different astronomical objects such as galaxies, black holes, and stellar objects. By comparing the observations from a source at different frequencies with template models, astronomers are able to infer the type of this observed object. In this paper, we take a Bayesian model averaging perspective to learn astronomical objects, employing a Bayesian nonparametric approach to accommodate the deviation from convex combinations of known log-SEDs. To effectively use telescope time for observations, we then study Bayesian nonparametric sequential experimental design without conjugacy, in which we use sequential Monte Carlo as an efficient tool to maximize the volume of information stored in the posterior distribution of the parameters of interest. A new technique for performing inferences in log-Gaussian Cox processes called the Poisson log-normal approximation is also proposed. Simulations show the speed, accuracy, and usefulness of our method. While the strategy we propose in this paper is brand new in the astronomy literature, the inferential techniques developed apply to more general nonparametric sequential experimental design problems.