相关论文: The Spend-It-All Region and Small Time Results for…
An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper is devoted to the study of the max K-armed bandit problem, which consists in sequentially allocating resources in order to detect extreme values. Our contribution is twofold. We first significantly refine the analysis of the…
In $\mathcal{X}$-armed bandit problem an agent sequentially interacts with environment which yields a reward based on the vector input the agent provides. The agent's goal is to maximise the sum of these rewards across some number of time…
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…
One of the classic data mining tasks is to discover bursts, time intervals, where events occur at abnormally high rate. In this paper we revisit Kleinberg's seminal work, where bursts are discovered by using exponential distribution with a…
We study a stochastic budget-allocation problem over $K$ tasks. At each round $t$, the learner chooses an allocation $X_t \in \Delta_K$. Task $k$ succeeds with probability $F_k(X_{t,k})$, where $F_1,\dots,F_K$ are nondecreasing…
The finite colliding bullets problem is the following simple problem: consider a gun, whose barrel remains in a fixed direction; let $(V_i)_{1\le i\le n}$ be an i.i.d.\ family of random variables with uniform distribution on $[0,1]$; shoot…
The celebrated multi-armed bandit problem in decision theory models the basic trade-off between exploration, or learning about the state of a system, and exploitation, or utilizing the system. In this paper we study the variant of the…
We consider the infinite-horizon, average-reward restless bandit problem in discrete time. We propose a new class of policies that are designed to drive a progressively larger subset of arms toward the optimal distribution. We show that our…
We provide a tight bound on the amount of experimentation under the optimal strategy in sequential decision problems. We show the applicability of the result by providing a bound on the cut-off in a one-arm bandit problem.
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 consider optimal sequential allocation in the context of the so-called stochastic multi-armed bandit model. We describe a generic index policy, in the sense of Gittins [J. R. Stat. Soc. Ser. B Stat. Methodol. 41 (1979) 148-177], based on…
In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
This paper considers a multi-armed bandit game where the number of arms is much larger than the maximum budget and is effectively infinite. We characterize necessary and sufficient conditions on the total budget for an algorithm to return…
This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…