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We address structured covariance estimation in Elliptical distribution. We assume it is a priori known that the covariance belongs to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of…

Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…

Multi-dimensional online decision making plays a crucial role in many real applications such as online recommendation and digital marketing. In these problems, a decision at each time is a combination of choices from different types of…

Restless bandit problems assume time-varying reward distributions of the arms, which adds flexibility to the model but makes the analysis more challenging. We study learning algorithms over the unknown reward distributions and prove a…

This paper studies performative risk minimization, a formulation of stochastic optimization under decision-dependent distributions. We consider the general case where the performative risk can be non-convex, for which we develop efficient…

A key goal in stochastic contextual linear bandits is to efficiently learn a near-optimal policy. Prior algorithms for this problem learn a policy by strategically sampling actions but naively (passively) sampling contexts from the…

Standard bandit algorithms that assume continual reallocation of measurement effort are challenging to implement due to delayed feedback and infrastructural/organizational difficulties. Motivated by practical instances involving a handful…

We address multi-armed bandits (MAB) where the objective is to maximize the cumulative reward under a probabilistic linear constraint. For a few real-world instances of this problem, constrained extensions of the well-known Thompson…

Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Information-directed sampling (IDS) is a powerful framework for solving bandit problems which has shown strong results in both Bayesian and frequentist settings. However, frequentist IDS, like many other bandit algorithms, requires that one…

This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…

Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

This paper considers stochastic linear bandits with general nonlinear constraints. The objective is to maximize the expected cumulative reward over horizon $T$ subject to a set of constraints in each round $\tau\leq T$. We propose a…

Non-stationarity is ubiquitous in human behavior and addressing it in the contextual bandits is challenging. Several works have addressed the problem by investigating semi-parametric contextual bandits and warned that ignoring…

We study a stochastic bandit algorithm motivated by retry-aware objectives that value the best outcome among multiple attempts, such as pass@$k$ and max@$k$. Given a posterior over arm values, ReMax chooses a sampling distribution that…

We propose ${\tt AdaTS}$, a Thompson sampling algorithm that adapts sequentially to bandit tasks that it interacts with. The key idea in ${\tt AdaTS}$ is to adapt to an unknown task prior distribution by maintaining a distribution over its…

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…