Related papers: Pure Exploration with Infinite Answers
This paper introduces the framework of multi-armed sampling, which serves as the sampling counterpart to the optimization problem of multi-armed bandits. Our primary motivation is to rigorously examine the exploration-exploitation trade-off…
Motivated by real-world applications such as fast fashion retailing and online advertising, the Multinomial Logit Bandit (MNL-bandit) is a popular model in online learning and operations research, and has attracted much attention in the…
In pure-exploration problems, information is gathered sequentially to answer a question on the stochastic environment. While best-arm identification for linear bandits has been extensively studied in recent years, few works have been…
Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model.…
We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state $y_d$, and a desired control $u_d$. It is proved that such problems are always nonuniquely solvable…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
In active sequential testing, also termed pure exploration, a learner is tasked with the goal to adaptively acquire information so as to identify an unknown ground-truth hypothesis with as few queries as possible. This problem, originally…
In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on current state and an entropy-regularized term is added to the reward functional. Such a…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
We study the Combinatorial Pure Exploration problem with Continuous and Separable reward functions (CPE-CS) in the stochastic multi-armed bandit setting. In a CPE-CS instance, we are given several stochastic arms with unknown distributions,…
We investigate stochastic differential games of optimal trading comprising a finite population. There are market frictions in the present framework, which take the form of stochastic permanent and temporary price impacts. Moreover,…
We study the problem of regression with interval targets, where only upper and lower bounds on target values are available in the form of intervals. This problem arises when the exact target label is expensive or impossible to obtain, due…
We introduce the "inverse bandit" problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement…
Reinforcement Learning has emerged as a strong alternative to solve optimization tasks efficiently. The use of these algorithms highly depends on the feedback signals provided by the environment in charge of informing about how good (or…
Recent work on exploration in reinforcement learning (RL) has led to a series of increasingly complex solutions to the problem. This increase in complexity often comes at the expense of generality. Recent empirical studies suggest that,…
This paper investigates the Nash equilibrium of a bi-objective optimal control problem governed by the Stokes equations. A multi-objective Nash strategy is formulated, and fundamental theoretical results are established, including the…
Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains…
Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision-making and search under uncertainty. In modern applications, however, one is often faced with a tremendously large number of options. Even…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
The problem of finding the sparsest solution to a linear underdetermined system of equations, often appearing, e.g., in data analysis, optimal control, system identification, or sensor selection problems, is considered. This non-convex…