Some aspects of the sequential design of experiments

By H. Robbins. 1952

Until recently, statistical theory has been restricted to the design and analysis of sampling experiments in which the size and composition of the samples are completely determined before the experimentation begins. The reasons for this are partly historical, dating back to the time when the statistician was consulted, if at all, only after the experiment was over, and partly intrinsic in the mathematical difficulty of working with anything but a fixed number of independent random variables. A major advance now appears to be in the making with the creation of a theory of the sequential design of experiments, in which the size and composition of the samples are not fixed in advance but are functions of the observations themselves.

Subfields: Statistics and Probability

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Citations in the corpus

Benchmark and Survey of Automated Machine Learning Frameworks (2019, background): “The selection of a hyperpartition can be modeled as a multi-armed bandit problem (Robbins, 1952).”
Survey on Automated Machine Learning (2019, background): “An extensively studied model for this problem is the multi-armed bandit problem (Robbins, 1952).”
Counterfactual reasoning and learning systems: the example of computational advertising (2012, background): “• In the multi-armed bandit (Robbins, 1952), a user-defined policy function π determines the distribution of action a ∈ {1 .”
Doubly Robust Policy Evaluation and Optimization (2014, background): “1Parts of this paper were presented at the 28th International Conference on Machine Learning (Dudík, Langford and Li, 2011), and the 28th Conference on Uncertainty in Artificial Intelligence (Dudík et al., 2012). dits introduced by Robbins (1952).”
Unbiased offline evaluation of contextual-bandit-based news article recommendation algorithms (2010, background): “Furthermore, by decaying ǫ appropriately, the per-step regret, R A ( T ) /T , converges to 0 with probability 1 [23].”
Introduction to Online Convex Optimization (2016, background): “The Multi-Armed Bandit problem has history going back more than fifty years to the work of Robbins (90), see the survey of (25) for a much more detailed history.”
The offset tree for learning with partial labels (2008, background): “The problem considered here is a non-interactive version of the contextual bandit problem (see [2, 3, 5, 15, 20] for background on the bandit problem).”
Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems (2012, neutral): “In the original formalization of Robbins [1952], which builds on the work of Wald [1947] —see also Arrow et al.”
Fair Algorithms for Infinite and Contextual Bandits (2016, background): “ved; this models the fact that a bank does not observe whether an individual denied a loan would have paid it back. This setting is a generalization of the classical \multi-armed bandit" problem [28, 29, 21] called the contextual bandit problem [23, 10]. Our main theoretical results are positiv”
Parallelizing Exploration-Exploitation Tradeoffs with Gaussian Process Bandit Optimization (2012, background): “Related Work Classical work on multi-armed bandit problems has focused on the case of a finite number of decisions (Robbins, 1952).”
On the Complexity of Best-Arm Identification in Multi-Armed Bandit Models (2014, background): “…regret up to horizon t ≥ 1 deﬁned as R t ( ν ) = tµ [1] − ν =1 Z s . paradigmatic Regret minimization, which is paradigmatic of the so-called exploration versus exploitation dilemma , was introduced by Robbins (1952) and its complexity is well understood for simple families of parametric bandits.”
Ad Hoc Autonomous Agent Teams: Collaboration without Pre-Coordination (2010, background): “They formalize this situation as an instance of the well-studied k-armed bandit problem (Robbins 1952).”
The Convolutional Tsetlin Machine (2019, methodology): “It is based on the Tsetlin Automaton (TA) [36], one of the pioneering solutions to the well-known multi-armed bandit problem [33, 11] and the ﬁrst Finite State Learning Automaton (FSLA) [25].”
Better Algorithms for Benign Bandits (2009, background): “Robbins [17] pioneered the study of various stochastic cost functions, followed by Hannan [10], Lai and Robbins [13] and others.”
Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges (2015, methodology): “Their roots can be traced back to work produced by Thompson (1933), which was later continued and developed in Robbins (1952), Bellman (1956), and ﬁnally Gittins and Jones (1974).”