Related papers: Bounds on Query Convergence
In this paper, we propose a learning approach to analyze dynamic systems with asymmetric information structure. Instead of adopting a game theoretic setting, we investigate an online quadratic optimization problem driven by system noises…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
We study the framework of a dynamic decision-making scenario with resource constraints. In this framework, an agent, whose target is to maximize the total reward under the initial inventory, selects an action in each round upon observing a…
Consider the classical problem of predicting the next bit in a sequence of bits. A standard performance measure is {\em regret} (loss in payoff) with respect to a set of experts. For example if we measure performance with respect to two…
This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
The expected regret of any reinforcement learning algorithm is lower bounded by $\Omega\left(\sqrt{DXAT}\right)$ for undiscounted returns, where $D$ is the diameter of the Markov decision process, $X$ the size of the state space, $A$ the…
We study the problem of preferential Bayesian optimization (BO), where we aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. Inspired by the likelihood ratio idea, we construct a…
This work theoretically studies a ubiquitous reinforcement learning policy for controlling the canonical model of continuous-time stochastic linear-quadratic systems. We show that randomized certainty equivalent policy addresses the…
The limits of quantum feedback control have immediate consequences for quantum information science at large, yet remain largely unexplored. Here, we combine quantum filtering theory and moment-sum-of-squares techniques to construct a…
Constrained Online Convex Optimization (COCO) can be seen as a generalization of the standard Online Convex Optimization (OCO) framework. At each round, a cost function and constraint function are revealed after a learner chooses an action.…
We establish fundamental limits on estimation accuracy for the noisy 20 questions problem with measurement-dependent noise and introduce optimal non-adaptive procedures that achieve these limits. The minimal achievable resolution is defined…
We study the problem of incentive-compatible online learning with bandit feedback. In this class of problems, the experts are self-interested agents who might misrepresent their preferences with the goal of being selected most often. The…
In many areas of medicine, security, and life sciences, we want to allocate limited resources to different sources in order to detect extreme values. In this paper, we study an efficient way to allocate these resources sequentially under…
Bayesian optimization (BO) with preference-based feedback has recently garnered significant attention due to its emerging applications. We refer to this problem as Bayesian Optimization from Human Feedback (BOHF), which differs from…
We consider a bandit optimization problem for nonconvex and non-smooth functions, where in each trial the loss function is the sum of a linear function and a small but arbitrary perturbation chosen after observing the player's choice. We…
Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven success in applications for decades, important open questions remain on the theoretical convergence behaviors…
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…
This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under…
Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the…