Online convex optimization in the bandit setting: gradient descent without a gradient Export

@misc{citeulike:761844, abstract = {We consider a the general online convex optimization framework introduced by Zinkevich. In this setting, there is a sequence of convex functions. Each period, we must choose a signle point (from some feasible set) and pay a cost equal to the value of the next function on our chosen point. Zinkevich shows that, if the each function is revealed after the choice is made, then one can achieve vanishingly small regret relative the best single decision chosen in hindsight. <br />We extend this to the bandit setting where we do not find out the entire functions but rather just their value at our chosen point. We show how to get vanishingly small regret in this setting. <br />Our approach uses a simple approximation of the gradient that is computed from evaluating a function at a single (random) point. We show that this estimate is sufficient to mimic Zinkevich's gradient descent online analysis, with access to the gradient (only being able to evaluate the function at a single point).}, archivePrefix = {arXiv}, author = {Flaxman, Abraham D. and Kalai, Adam T. and Mcmahan, Brendan H.}, citeulike-article-id = {761844}, citeulike-linkout-0 = {http://arxiv.org/abs/cs.LG/0408007}, citeulike-linkout-1 = {http://arxiv.org/pdf/cs.LG/0408007}, day = {2}, eprint = {cs.LG/0408007}, month = {Aug}, posted-at = {2007-05-10 18:50:34}, priority = {0}, title = {Online convex optimization in the bandit setting: gradient descent without a gradient}, url = {http://arxiv.org/abs/cs.LG/0408007}, year = {2004} }

TY - ELEC ID - citeulike:761844 L3 - citeulike-article-id:761844 N2 - We consider a the general online convex optimization framework introduced by Zinkevich. In this setting, there is a sequence of convex functions. Each period, we must choose a signle point (from some feasible set) and pay a cost equal to the value of the next function on our chosen point. Zinkevich shows that, if the each function is revealed after the choice is made, then one can achieve vanishingly small regret relative the best single decision chosen in hindsight. <br />We extend this to the bandit setting where we do not find out the entire functions but rather just their value at our chosen point. We show how to get vanishingly small regret in this setting. <br />Our approach uses a simple approximation of the gradient that is computed from evaluating a function at a single (random) point. We show that this estimate is sufficient to mimic Zinkevich's gradient descent online analysis, with access to the gradient (only being able to evaluate the function at a single point). TI - Online convex optimization in the bandit setting: gradient descent without a gradient AU - Flaxman, Abraham AU - Kalai, Adam AU - Mcmahan, Brendan PY - 2004/Aug/02/ UR - http://arxiv.org/abs/cs.LG/0408007 ER -