Optimal and Efficient Dynamic Regret Algorithms for Non-Stationary Dueling Bandits [article]

Shubham Gupta, Aadirupa Saha
<span title="2021-11-06">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the problem of 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(√(KT)) high
more &raquo; ... ility regret. 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 establish (√(SKT)) and (V_T^1/3K^1/3T^2/3) dynamic-regret guarantees, S being the total number of 'effective-switches' in the underlying preference relations and V_T being a measure of 'continuous-variation' non-stationarity. The complexity of these problems have not been studied prior to this work despite the practicability of non-stationary environments in real world systems. We justify the optimality of our algorithms by proving matching lower bound guarantees under both the above-mentioned notions of non-stationarities. Finally, we corroborate our results with extensive simulations and compare the efficacy of our algorithms over state-of-the-art baselines.
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