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

@inproceedings{Saha2019FromPT, title={From PAC to Instance-Optimal Sample Complexity in the Plackett-Luce Model}, author={Aadirupa Saha and Aditya Gopalan}, booktitle={International Conference on Machine Learning}, year={2019} }

We consider PAC-learning a good item from $k$-subsetwise feedback information sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance. In the setting where subsets of a fixed size can be tested and top-ranked feedback is made available to the learner, we give an algorithm with optimal instance-dependent sample complexity, for PAC best arm identification, of $O\bigg(\frac{\theta_{[k]}}{k}\sum_{i = 2}^n\max\Big(1,\frac{1}{\Delta_i^2}\Big) \ln\frac{k…

## 7 Citations

### The Sample Complexity of Best-k Items Selection from Pairwise Comparisons

- Computer ScienceICML
- 2020

This paper studies the sample complexity (aka number of comparisons) bounds for the active best-$k$ items selection from pairwise comparisons and proposes two algorithms based on PAC best items selection algorithms that works for $k=1 and is sample complexity optimal up to a loglog factor.

### On Sample Complexity Upper and Lower Bounds for Exact Ranking from Noisy Comparisons

- Computer ScienceNeurIPS
- 2019

This paper aims at the exact ranking without knowledge on the instances, while most of the previous works either focus on approximate rankings or study exact ranking but require prior knowledge.

### Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences

- Computer ScienceArXiv
- 2022

This work proposes a novel reduction from any (general) dueling bandits to multi-armed bandits and despite the simplicity, it allows us to improve many existing results in Dueling bandits.

### Versatile Dueling Bandits: Best-of-both World Analyses for Online Learning from Relative Preferences

- Computer Science
- 2022

The robustness of the proposed algorithm is justified by proving its optimal regret rate under adversarially corrupted preferences—this outperforms the existing state-of-the-art corrupted dueling results by a large margin.

### Finding Optimal Arms in Non-stochastic Combinatorial Bandits with Semi-bandit Feedback and Finite Budget

- Computer Science, MathematicsArXiv
- 2022

A generic algorithm suitable to cover the full spectrum of conceivable arm elimination strategies from aggressive to conservative is suggested and theoretical questions about thecient and necessary budget of the algorithm to choose the best arm are answered and complemented by deriving lower bounds for any learning algorithm for this problem scenario.

### Sample Complexity Bounds for Active Ranking from Multi-wise Comparisons

- Computer Science
- 2021

Whether and to what degree utilizing multi-wise comparisons can reduce the sample complexity for the ranking problems compared to ranking from pairwise comparisons is helps understand.

### Identification of the Generalized Condorcet Winner in Multi-dueling Bandits

- Computer ScienceNeurIPS
- 2021

The Dvoretzky–Kiefer–Wolfowitz tournament (DKWT) algorithm is proposed, which proves to be nearly optimal and empirically outperforms current state-of-the-art algorithms, even in the special case of dueling bandits or under a Plackett-Luce assumption on the feedback mechanism.

### One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits

- Computer ScienceArXiv
- 2022

This work proposes a new notion of Internal Regret for sleeping MAB, and proposes an algorithm that yields sublinear regret in that measure, even for a completely adversarial sequence of losses and availabilities.

### Online Elicitation of Necessarily Optimal Matchings

- Computer Science, EconomicsAAAI
- 2022

This paper investigates the elicitation of necessarily Pareto optimal (NPO) and necessarily rank-maximal (NRM) matchings and answers an open question and gives an online algorithm for eliciting an NRM matching in the next-best query model which is 3/2-competitive.

### ANACONDA: An Improved Dynamic Regret Algorithm for Adaptive Non-Stationary Dueling Bandits

- Computer ScienceArXiv
- 2022

An elimination-based rescheduling algorithm is developed and shown to be a near-optimal dynamic regret bound, where S CW is the number of times the Condorcet winner changes in T rounds.

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