Related papers: Pure Exploration with Infinite Answers
We study a novel pure exploration problem: the $\epsilon$-Thresholding Bandit Problem (TBP) with fixed confidence in stochastic linear bandits. We prove a lower bound for the sample complexity and extend an algorithm designed for Best Arm…
We study pure exploration with infinitely many bandit arms generated i.i.d. from an unknown distribution. Our goal is to efficiently select a single high quality arm whose average reward is, with probability $1-\delta$, within $\varepsilon$…
A lot of research activity has recently taken place around the chase procedure, due to its usefulness in data integration, data exchange, query optimization, peer data exchange and data correspondence, to mention a few. As the chase has…
Pure exploration is one of the fundamental problems in multi-armed bandits (MAB). However, existing works mostly focus on specific pure exploration tasks, without a holistic view of the general pure exploration problem. This work fills this…
We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the…
We revisit the problem of stochastic online learning with feedback graphs, with the goal of devising algorithms that are optimal, up to constants, both asymptotically and in finite time. We show that, surprisingly, the notion of optimal…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
Realistic environments often provide agents with very limited feedback. When the environment is initially unknown, the feedback, in the beginning, can be completely absent, and the agents may first choose to devote all their effort on…
The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >=…
We study the problem of infrequent exploration in linear bandits, addressing a significant yet overlooked gap between fully adaptive exploratory methods (e.g., UCB and Thompson Sampling), which explore potentially at every time step, and…
The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty.…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
The chase algorithm is a fundamental tool for query evaluation and query containment under constraints, where the constraints are (sub-classes of) tuple-generating dependencies (TGDs) and equality generating depencies (EGDs). So far, most…
Contextual bandits can solve a huge range of real-world problems. However, current popular algorithms to solve them either rely on linear models, or unreliable uncertainty estimation in non-linear models, which are required to deal with the…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
We consider online learning problems under a partial observability model capturing situations where the information conveyed to the learner is between full information and bandit feedback. In the simplest variant, we assume that in addition…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…