# PAC Battling Bandits in the Plackett-Luce Model

@inproceedings{Saha2018PACBB, title={PAC Battling Bandits in the Plackett-Luce Model}, author={Aadirupa Saha and Aditya Gopalan}, booktitle={International Conference on Algorithmic Learning Theory}, year={2018} }

We introduce the probably approximately correct (PAC) \emph{Battling-Bandit} problem with the Plackett-Luce (PL) subset choice model--an online learning framework where at each trial the learner chooses a subset of $k$ arms from a fixed set of $n$ arms, and subsequently observes a stochastic feedback indicating preference information of the items in the chosen subset, e.g., the most preferred item or ranking of the top $m$ most preferred items etc. The objective is to identify a near-best item…

## 21 Citations

### From PAC to Instance-Optimal Sample Complexity in the Plackett-Luce Model

- Computer ScienceICML
- 2020

This work considers PAC-learning a good item from $k$-subsetwise feedback information sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance, and gives an algorithm with optimal instance- dependent sample complexity for PAC best arm identification.

### Preselection Bandits under the Plackett-Luce Model

- Computer ScienceArXiv
- 2019

This paper introduces the Preselection Bandit problem, in which the learner preselects a subset of arms for a user, which then chooses the final arm from this subset, and proposes algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

### Combinatorial Bandits with Relative Feedback

- Computer Science, MathematicsNeurIPS
- 2019

We consider combinatorial online learning with subset choices when only relative feedback information from subsets is available, instead of bandit or semi-bandit feedback which is absolute.…

### Best-item Learning in Random Utility Models with Subset Choices

- Computer ScienceAISTATS
- 2020

Fundamental lower bounds on PAC sample complexity show that the learning algorithm given, based on pairwise relative counts of items and hierarchical elimination, is near-optimal in terms of its dependence on $n,k$ and $c$.

### Preselection Bandits

- Computer ScienceICML
- 2020

This paper introduces the Preselection Bandit problem, in which the learner preselects a subset of arms for a user, which then chooses the final arm from this subset, and proposes algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

### Adversarial Dueling Bandits

- Computer ScienceICML
- 2021

The problem of regret minimization in Adversarial Dueling Bandits is introduced, and an algorithm whose $T$-round regret compared to the \emph{Borda-winner} from a set of $K$ items is $\tilde{O}(K^{1/3}T^{2/3})$, as well as a matching $\Omega(K/\Delta^2)$ lower bound.

### Online Preselection with Context Information under the Plackett-Luce Model

- Computer ScienceArXiv
- 2020

An extension of the contextual multi-armed bandit problem, in which, instead of selecting a single alternative (arm), a learner is supposed to make a preselection in the form of a subset of alternatives, the CPPL algorithm is proposed, which is inspired by the well-known UCB algorithm.

### Regret Minimization in Stochastic Contextual Dueling Bandits

- Computer ScienceArXiv
- 2020

This work is the first to consider the problem of regret minimization of contextual dueling bandits for potentially infinite decision spaces and gives provably optimal algorithms along with a matching lower bound analysis.

### Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability

- Computer ScienceALT
- 2022

A new algorithm is provided that achieves the optimal regret rate for a new notion of best response regret, which is a strictly stronger performance measure than those considered in prior works.

### Choice Bandits

- Computer ScienceNeurIPS
- 2020

An algorithm for choice bandits, termed Winner Beats All (WBA), with a distribution dependent O(log T ) regret bound under all these choice models is proposed, which is competitive with previous dueling bandit algorithms and outperforms the recently proposed MaxMinUCB algorithm designed for the MNL model.

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