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Poster
Dueling Bandits with Adversarial Sleeping
Aadirupa Saha · Pierre Gaillard

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @ None #None
We introduce the problem of sleeping dueling bandits with stochastic preferences and adversarial availabilities (DB-SPAA). In almost all dueling bandit applications, the decision space often changes over time; eg, retail store management, online shopping, restaurant recommendation, search engine optimization, etc. Surprisingly, this sleeping aspect' of dueling bandits has never been studied in the literature. Like dueling bandits, the goal is to compete with the best arm by sequentially querying the preference feedback of item pairs. The non-triviality however results due to the non-stationary item spaces that allow any arbitrary subsets items to go unavailable every round. The goal is to find an optimal no-regret policy that can identify the best available item at each round, as opposed to the standard fixed best-arm regret objective' of dueling bandits. We first derive an instance-specific lower bound for DB-SPAA $\Omega( \sum_{i =1}^{K-1}\sum_{j=i+1}^K \frac{\log T}{\Delta(i,j)})$, where $K$ is the number of items and $\Delta(i,j)$ is the gap between items $i$ and $j$. This indicates that the sleeping problem with preference feedback is inherently more difficult than that for classical multi-armed bandits (MAB). We then propose two algorithms, with near optimal regret guarantees. Our results are corroborated empirically.

#### Author Information

##### Aadirupa Saha (Microsoft Research)

Aadirupa Saha is a PhD student at the department of Computer Science and Automation (CSA), Indian Institute of Science (IISc), Bangalore and was a research intern at Google, Mountain View, CA (June-Sept, 2019). Her research interests broadly lie in the areas of Machine Learning, Statistical Learning Theory and Optimization. Her current research specifically focuses on decision making under uncertainty from sequential data, reinforcement learning, and preference based rank aggregation problems.