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在线线性优化算法

Bandit Algorithms for Online Linear Optimization
课程网址: http://videolectures.net/icml09_cesa_bianchi_itbaolo/  
主讲教师: Nicolò Cesa-Bianchi
开课单位: 米兰大学
开课时间: 2009-08-26
课程语种: 英语
中文简介:
在在线线性优化问题中, 预报员在每个实例中选择一个来自 d 维欧几里得空间的特定子集 s 的向量 x, 并遭受 x 中线性的时间依赖性损失。预报员的目标是实现这一目标, 从长远来看, 累积损失不会比 s 中最好的矢量大多少。在本次讨论中, 我们考虑了线性优化问题的 "的强盗" 设置, 在这种设置中, 预报员只能访问所选择的向量的损失。我们调查了一些最近解决这个问题的算法。对于 s 是 d 维布尔超立方体子集的特殊情况, 我们描述了一个新的预测器, 它的性能对于各种具体的 s 选择来说, 比所有以前已知的边界都要好, 一般情况下也不是可以改进的。我们还指出, 对于各种有趣的 s 选择, 存在计算效率高的实现。与加博尔·卢戈西 (巴塞罗那) 共同工作。
课程简介: In the online linear optimization problem a forecaster chooses, at each time instance, a vector x from a certain given subset S of the D-dimensional Euclidean space and suffers a time-dependent loss that is linear in x. The goal of the forecaster is to achieve that, in the long run, the accumulated loss is not much larger than that of the best possible vector in S. In this talk we consider the "bandit" setting of the linear optimization problem, in which the forecaster has only access to the losses of the chosen vectors. We survey some recent algorithms that solve this problem. For the special case in which S is a subset of the d-dimensional Boolean hypercube, we describe a new forecaster whose performance, for a variety of concrete choices of S, is better than all previously known bounds, and not improvable in general. We also point out that computationally efficient implementations for various interesting choices of S exist. Joint work with Gabor Lugosi (Barcelona).
关 键 词: 非线性优化问; 线性规划优化方法; 欧氏空间
课程来源: 视频讲座网
最后编审: 2020-06-06:毛岱琦(课程编辑志愿者)
阅读次数: 524