Adaptive treatment allocation and the multi-armed bandit problem

By Tze Leung Lai. 1987

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In Reinforcement Learning

Citations in the corpus

Degenerate Feedback Loops in Recommender Systems (2019, background): “• Upper Conﬁdence Bound Multi-armed Bandit Algorithm ( UCB ) (Lai, 1987 i.e. ˆ c t ( a ) = t 0 ≤ i ≤ t,a ∈ a i c t ( a ) /T a ( t ) , and T a ( t ) is the number of times item a has been served up to time t , i.e.”
Learning to Optimize via Posterior Sampling (2013, positive): “Indeed, algorithms based on this principle have been shown to be asymptotically efficient in terms of both regret (Lai and Robbins [26]) and Bayesian regret (Lai [25]), to satisfy order optimal minimax regret bounds (Audibert and Bubeck [8]), to satisfy order optimal bounds on regret and Bayesian re”
On Bayesian Upper Confidence Bounds for Bandit Problems (2012, background): “We show that the Bayes- UCB algorithm is optimal, in the sense that it reaches the lower-bound (2) of Lai and Robbins.”
Regret Lower Bound and Optimal Algorithm in Dueling Bandit Problem (2015, background): “Third, in the standard bandit problem, it is reported that KL-UCB+ (Lai, 1987; Garivier and Cappé, 2011) performs better than DMED.”
A modern Bayesian look at the multi-armed bandit (2010, methodology): “Although it is hard to compute Gittins indices exactly, Brezzi and Lai [14] have developed an approximate Gittins index based on a normal approximation to p(|y).”
Learning to Optimize via Information-Directed Sampling (2014, methodology): “To set the stage for our discussion, we introduce UCB algorithms and Thompson sampling in the next subsection.”
An Asymptotically Optimal Multi-Armed Bandit Algorithm and Hyperparameter Optimization (2020, background): “Moreover, if π is uniformly good and some additional regularity conditions are satisfied, Lai and Robbins (1985) provided a lower bound of the growth rate:”
A Linear Response Bandit Problem (2013, methodology): “In that setting, see Lai (1987), patients enter sequentially and receive one of, say, two possible treatments whose efficacy is yet to be determined.”
SEQUENTIAL ANALYSIS: SOME CLASSICAL PROBLEMS AND NEW CHALLENGES (2001, background): “There is also an analogous asymptotic theory for the discounted multi-armed bandit problem as β → 1, as shown by Chang and Lai (1987).”
Bandit Algorithms (2020, background): “The sequential form that appears in the above exercise is based on Lemma 2 of Lai and Robbins [1985] who cite Robbins and Siegmund [1972] as the original source.”
Linearly Parameterized Bandits (2008, background): “This assumption enables us to decompose the problem, leading to policies that consider each arm separately. In their seminal papers, Lai and Robbins (1985) and Lai (1987) propose an asymptotically optimal policy that maintains an index for each arm and selects in each period the arm with the highest”