The Continuum-Armed Bandit Problem

By Rajeev Agrawal. 1995

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Citations in the corpus

Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data (2016, neutral): “values instead of discrete steps [79], [80].”
The value of knowing a demand curve: bounds on regret for online posted-price auctions (2003, background): “However the best known upper bound is due to Agrawal [1], who describes an algorithm achieving regret O(n) in the case that the expected reward is a differentiable function of t.”
Multi-armed bandits in metric spaces (2008, methodology): “While our work is the first to treat the Lipschitz MAB problem in general metric spaces, special cases of the problem are implicit in prior work on the continuum-armed bandit problem [1, 4, 9, 15] — which corresponds to the space [0, 1] under the metric Ld(x, y) = |x − y|, d ≥ 1 — and the experiment”
X-Armed Bandits (2010, unknown): “During the last decades numerous authors have investigated such “continuum-armed” bandit problems [3; 21; 6; 22; 12].”
Introduction to Multi-Armed Bandits (2019, background): “t bound is given in (4.11). Since the algorithm does not depend on , this bound holds for all >0. 4.4 Bibliographic remarks and further directions Continuum-armed bandits have been introduced in Agrawal (1995), and further studied in (Kleinberg, 2004; Auer et al., 2007). Uniform discretization ha”
Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Arms (2014, unknown): “Since our work in Chen et al. (2013), several studies are also related to combinatorial multi-armed bandits or in general combinatorial online learning.”
Nearly Tight Bounds for the Continuum-Armed Bandit Problem (2004, methodology): “For a one-dimensional strategy space, the first algorithm with sublinear regret appeared in [1], while the first polynomial lower bound on regret appeared in [15].”
Regret Bounds for Gaussian Process Bandit Problems (2010, unknown): “Diﬀerent approaches to the continuum arm space setting have already been proposed Agrawal (1995); Kleinberg (2004)”
Combining active learning and reactive control for robot grasping (2010, background): “From a machine learning perspective, this selecting of grasps can be interpreted as a continuum-armed bandits problem [1].”
Contextual Bandits with Similarity Information (2009, background): “Following the work in [2, 20, 5, 24] on the (non-contextual) bandits, a particularly simple way to represent similarity information in the contextual bandit setting is via a similarity distance between the context-arm pairs, gives an upper bound on the difference between the corresponding payoffs.”
Stochastic Convex Optimization with Bandit Feedback (2011, methodology): “For instance, the f is assumed to be linear in the paper [9], a Lipschitz condition on f is assumed in the works [3, 12, 13], and Srinivas et al.”
From Bandits to Monte-Carlo Tree Search: The Optimistic Principle Applied to Optimization and Planning (2014, background): “• Optimistic exploration: Select the arm with the largest high-probability upper-confidence-bound (initiated by Lai and Robbins [1985], Agrawal [1995b], Burnetas and Katehakis [1996a]), an example of which is the UCB algorithm [Auer et al.”
Bandits with Knapsacks (2013, methodology): “UCB1 algorithm [6]. Subsequent work supplied algorithms for stochastic MAB problems in which the set of arms is inﬁnite and the payoff function is linear [1, 15], concave [2], or Lipschitz-continuous [3, 8, 13, 25, 29, 28]. Conﬁdence bound techniques have been an integral part of all these works, an”