Understand
The generalized linear bandit framework has attracted a lot of attention in recent years by extending the well-understood linear setting and allowing to model richer reward structures.
- It notably covers the logistic model, widely used when rewards are binary.
- For logistic bandits, the frequentist regret guarantees of existing algorithms are $\tilde{\mathcal{O}}(\kappa \sqrt{T})$, where $\kappa$ is a problem-dependent constant.
- Unfortunately, $\kappa$ can be arbitrarily large as it scales exponentially with the size of the decision set.
Built on
Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws
de la Pena, V. H., Klass, M. J., and Lai, T. L. (2004) · 1933
Earlier work this paper cites.
Stochastic linear optimization under bandit feedback
Dani, V., Hayes, T. P., and Kakade, S. M. (2008) · 2008
Earlier work this paper cites.
Self-concordant analysis for logistic regression
Bach, F. et al. (2010) · 2010
Earlier work this paper cites.
Parametric Bandits: The Generalized Linear Case
Filippi, S., Cappe, O., Garivier, A., and Szepesvári, C. (2010) · 2010
Earlier work this paper cites.
Linearly parameterized bandits
Rusmevichientong, P. and Tsitsiklis, J. N. (2010) · 2010
Earlier work this paper cites.
Improved Algorithms for Linear Stochastic Bandits
Abbasi-Yadkori, Y., Pál, D., and Szepesvári, C. (2011) · 2011
Earlier work this paper cites.
Similar
Eluder dimension and the sample complexity of optimistic exploration
Russo, D. and Van Roy, B. (2013) · 2013
Cited alongside, same era.
Finite-time analysis of kernelised contextual bandits
Valko, M., Korda, N., Munos, R., Flaounas, I., and Cristianini, N. (2013) · 2013
Cited alongside, same era.
Learning to optimize via posterior sampling
Russo, D. and Van Roy, B. (2014) · 2014
Cited alongside, same era.
Linear thompson sampling revisited
Abeille, M., Lazaric, A., et al. (2017) · 2017
Cited alongside, same era.
Scalable generalized linear bandits: Online computation and hashing
Jun, K.-S., Bhargava, A., Nowak, R., and Willett, R. (2017) · 2017
Cited alongside, same era.
Then
An information-theoretic analysis for thompson sampling with many actions
Dong, S. and Van Roy, B. (2018) · 2018
Later among the works it cites.
Pg-ts: Improved thompson sampling for logistic contextual bandits
Dumitrascu, B., Feng, K., and Engelhardt, B. (2018) · 2018
Later among the works it cites.
Bandit algorithms
Lattimore, T. and Szepesvári, C. (2018) · 2018
Later among the works it cites.
On the performance of thompson sampling on logistic bandits
Dong, S., Ma, T., and Roy, B. V. (2019) · 2019
Later among the works it cites.
Provably optimal algorithms for generalized linear contextual bandits
Li, L., Lu, Y., and Zhou, D. (2017) · 2080
Closest in time.
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