Chasing Convex Bodies Optimally

Sellke, Mark

doi:10.48550/arxiv.1905.11968

Cited by 2 publications

(3 citation statements)

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“…( 4), thus showing a reduction from dynamic regret to convex body chasing, under only the Lipschitzness assumption on f t . Furthermore, recent work of (Sellke, 2019) shows that for any norm • * , there exists an algorithm with competitive ratio ω = d. This immediately implies the following new dynamic regret result.…”

Section: Further Reduction To Convex Body Chasingmentioning

confidence: 64%

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Improved Path-length Regret Bounds for Bandits

Bubeck,

Li,

Luo

et al. 2019

Preprint

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We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei and Luo, 2018) is in fact not improvable for adaptive adversary. Despite this negative result, we then develop two new algorithms, one that strictly improves over (Wei and Luo, 2018) with a smaller path-length measure, and the other which improves over for oblivious adversary when the path-length is large. Our algorithms are based on the well-studied optimistic mirror descent framework, but importantly with several novel techniques, including new optimistic predictions, a slight bias towards recently selected arms, and the use of a hybrid regularizer similar to that of .Furthermore, we extend our results to linear bandit by showing a reduction to obtaining dynamic regret for a full-information problem, followed by a further reduction to convex body chasing. As a consequence we obtain new dynamic regret results as well as the first path-length regret bounds for general linear bandit.

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Section: Further Reduction To Convex Body Chasingmentioning

confidence: 64%

“…4. According to (Sellke, 2019), when B * is the 2-norm ball, the dependence on d can be improved to √ d ln T .…”

Section: Corollary 6 Algorithm 3 With Option III Ensuresmentioning

confidence: 99%

Improved Path-length Regret Bounds for Bandits

Bubeck,

Li,

Luo

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore it is interesting to explore nonconvex and nonconcave nonstationary saddle point optimization problems in the online and bandit settings, by extending appropriately, the definitions of regret proposed in [RBGM19] for the argmin-type online nonconvex problems recently. Furthermore, recently the problem of convex body chasing, considered in [FL93] initially, has regained significant attention; see for example [BLLS19,Sel19,AGGT19]. It is intriguing to precisely formulate saddle-point versions of convex bodies chasing problem and explore algorithms for it.…”

Section: Discussionmentioning

confidence: 99%

Online and Bandit Algorithms for Nonstationary Stochastic Saddle-Point Optimization

Roy,

Chen,

Balasubramanian

et al. 2019

Preprint

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Saddle-point optimization problems are an important class of optimization problems with applications to game theory, multi-agent reinforcement learning and machine learning. A majority of the rich literature available for saddle-point optimization has focused on the offline setting. In this paper, we study nonstationary versions of stochastic, smooth, strongly-convex and strongly-concave saddle-point optimization problem, in both online (or first-order) and multi-point bandit (or zeroth-order) settings. We first propose natural notions of regret for such nonstationary saddle-point optimization problems. We then analyze extragradient and Frank-Wolfe algorithms, for the unconstrained and constrained settings respectively, for the above class of nonstationary saddle-point optimization problems. We establish sub-linear regret bounds on the proposed notions of regret in both the online and bandit setting.

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Chasing Convex Bodies Optimally

Cited by 2 publications

References 0 publications

Improved Path-length Regret Bounds for Bandits

Improved Path-length Regret Bounds for Bandits

Online and Bandit Algorithms for Nonstationary Stochastic Saddle-Point Optimization

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