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Optimal and Efficient Dynamic Regret Algorithms for Non-Stationary Dueling Bandits
Aadirupa Saha · Shubham Gupta

Tue Jul 19 08:50 AM -- 08:55 AM (PDT) @ Room 309
We study the problem of \emph{dynamic regret minimization} in $K$-armed Dueling Bandits under non-stationary or time-varying preferences. This is an online learning setup where the agent chooses a pair of items at each round and observes only a relative binary `win-loss' feedback for this pair sampled from an underlying preference matrix at that round. We first study the problem of static-regret minimization for adversarial preference sequences and design an efficient algorithm with $O(\sqrt{KT})$ regret bound. We next use similar algorithmic ideas to propose an efficient and provably optimal algorithm for dynamic-regret minimization under two notions of non-stationarities. In particular, we show $\tO(\sqrt{SKT})$ and $\tO({V_T^{1/3}K^{1/3}T^{2/3}})$ dynamic-regret guarantees, respectively, with $S$ being the total number of `effective-switches' in the underlying preference relations and $V_T$ being a measure of `continuous-variation' non-stationarity. These rates are provably optimal as justified with matching lower bound guarantees. Moreover, our proposed algorithms are flexible as they can be easily `blackboxed' to yield dynamic regret guarantees for other notions of dueling bandits regret, including condorcet regret, best-response bounds, and Borda regret. The complexity of these problems have not been studied prior to this work despite the practicality of non-stationary environments. Our results are corroborated with extensive simulations.

Author Information

Aadirupa Saha (TTI Chicago)

Bio: Aadirupa Saha is currently a visiting faculty at Toyota Technological Institute at Chicago (TTIC). She obtained her PhD from the Department of Computer Science, Indian Institute of Science, Bangalore, advised by Aditya Gopalan and Chiranjib Bhattacharyya. She spent two years at Microsoft Research New York City as a postdoctoral researcher. During her PhD, Aadirupa interned at Microsoft Research, Bangalore, Inria, Paris, and Google AI, Mountain View. Her research interests include Bandits, Reinforcement Learning, Optimization, Learning theory, Algorithms. She has organized various workshops, tutorials and also served as a reviewer in top ML conferences. Research Interests: Machine Learning Theory (specifically Online Learning, Bandits, Reinforcement Learning), Optimization, Game Theory, Algorithms. She is recently interested in exploring ML problems at the intersection of Fairness, Privacy, Game theory and Mechanism design.

Shubham Gupta (IBM Research)

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