Related papers: Universal Log-Optimality for General Classes of e-…
A classic problem in statistics is the estimation of the expectation of random variables from samples. This gives rise to the tightly connected problems of deriving concentration inequalities and confidence sequences, that is confidence…
We prove that a classic sub-Gaussian mixture proposed by Robbins in a stochastic setting actually satisfies a path-wise (deterministic) regret bound. For every path in a natural ``Ville event'' $\mathcal E_\alpha$, this regret till time $T$…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
Meta reinforcement learning sets a distribution over a set of tasks on which the agent can train at will, then is asked to learn an optimal policy for any test task efficiently. In this paper, we consider a finite set of tasks modeled…
The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
In this paper we consider the problem of universal {\em batch} learning in a misspecification setting with log-loss. In this setting the hypothesis class is a set of models $\Theta$. However, the data is generated by an unknown distribution…
Ensemble sampling serves as a practical approximation to Thompson sampling when maintaining an exact posterior distribution over model parameters is computationally intractable. In this paper, we establish a regret bound that ensures…
Many prediction domains, such as ad placement, recommendation, trajectory prediction, and document summarization, require predicting a set or list of options. Such lists are often evaluated using submodular reward functions that measure…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests…
The standard theory of optimal stopping is based on the idealised assumption that the underlying process is essentially known. In this paper, we drop this restriction and study data-driven optimal stopping for a general diffusion process,…
We study a class of adversarial bandit optimization problems in which the loss functions may be non-convex and non-smooth. In each round, the learner observes a loss that consists of an underlying linear component together with an…
E-values and E-processes (nonnegative supermartingales) provide anytime-valid evidence for sequential testing via Ville's inequality, yet their connection to Bayesian reasoning, representational structure, and computational feasibility are…
This paper presents the first non-asymptotic result showing that a model-free algorithm can achieve a logarithmic cumulative regret for episodic tabular reinforcement learning if there exists a strictly positive sub-optimality gap in the…
Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical…
Practitioners conducting adaptive experiments often encounter two competing priorities: maximizing total welfare (or `reward') through effective treatment assignment and swiftly concluding experiments to implement population-wide…
We consider the problem of sequentially maximizing an unknown function $f$ over a set of actions of the form $(s,\mathbf{x})$, where the selected actions must satisfy a safety constraint with respect to an unknown safety function $g$. We…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…