Batched Bandit Problems

@inproceedings{Perchet2015BatchedBP,
  title={Batched Bandit Problems},
  author={Vianney Perchet and Philippe Rigollet and Sylvain Chassang and Erik Snowberg},
  booktitle={COLT},
  year={2015}
}
Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits. 

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References

SHOWING 1-10 OF 62 REFERENCES
The multi-armed bandit problem with covariates
TLDR
This work introduces a policy called Adaptively Binned Successive Elimination (abse) that adaptively decomposes the global problem into suitably “localized” static bandit problems and introduces a nonparametric model where the expected rewards are smooth functions of the covariate and the hardness of the problem is captured by a margin parameter.
Bounded regret in stochastic multi-armed bandits
TLDR
A new randomized policy is proposed that attains a regret {\em uniformly bounded over time} in this setting and several lower bounds are proved, which show in particular that bounded regret is not possible if one only knows $\Delta$, and bounded regret of order $1/\Delta$ is not Possible.
Finite-time Analysis of the Multiarmed Bandit Problem
TLDR
This work shows that the optimal logarithmic regret is also achievable uniformly over time, with simple and efficient policies, and for all reward distributions with bounded support.
UCB revisited: Improved regret bounds for the stochastic multi-armed bandit problem
TLDR
For this modified UCB algorithm, an improved bound on the regret is given with respect to the optimal reward for K-armed bandits after T trials.
Asymptotically optimal multistage tests of simple hypotheses
A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling
Regret Bounds and Minimax Policies under Partial Monitoring
TLDR
The stochastic bandit game is considered, and it is proved that an appropriate modification of the upper confidence bound policy UCB1 (Auer et al., 2002a) achieves the distribution-free optimal rate while still having a distribution-dependent rate logarithmic in the number of plays.
A Model for Selecting One of Two Medical Treatments
Abstract A simple cost function approach is proposed for designing an optimal clinical trial when a total of N patients with a disease are to be treated with one of two medical treatments. The cost
Kullback–Leibler upper confidence bounds for optimal sequential allocation
TLDR
The main contribution is a unified finite-time analysis of the regret of these algorithms that asymptotically matches the lower bounds of Lai and Robbins (1985) and Burnetas and Katehakis (1996), respectively.
Sequential Experimentation in Clinical Trials: Design and Analysis
TLDR
The results suggest that the design of Sequential Testing Theory and Stochastic Optimization over Time in Clinical Trials with Failure-Time Endpoints is a good guide for designing Sequential Methods for Vaccine Safety Evaluation and Surveillance in Public Health.
Randomized Allocation of Treatments in Sequential Experiments
SUMMARY Since the idea of sequential allocation was first studied, in a version of what is now called the multi-armed bandit problem, the results of many investigations have shown that, even when an
...
1
2
3
4
5
...