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0111 · Mar 201919922001200920172026
5 results for supLinUCB

We study the linear contextual bandit problem with finite action sets. When the problem dimension is dd, the time horizon is TT, and there are n2d/2n \leq 2^{d/2} candidate actions per time period, we (1) show that the minimax expected regret is Ω(dT(logT)(logn))Ω(\sqrt{dT (\log T) (\log n)}) for every algorithm, and (2) introduce a V…

2019-03-30abs ↗pdf ↗

This paper addresses dueling bandits with contextual information, improving regret bounds by accounting for variance.

problem Minimizing cumulative regret in dueling bandits with contextual information.
method Proposes a new SupLinUCB-type algorithm for contextual dueling bandits with variance-aware regret bound.
result Achieves a variance-aware regret bound of ildeO(dt=1Tσt2+d) ilde O\big(d\sqrt{\sum_{t=1}^Tσ_t^2} + d\big).

A federated learning algorithm tackles linear bandits with adversarial actions, achieving optimal regret bounds.

problem Federated linear bandits with finite adversarial action sets.
method FedSupLinUCB algorithm, extending SupLinUCB and OFUL principles.
result Achieves a total regret of ildeO(dT) ilde{O}(\sqrt{d T}), matching minimax lower bound and being order-optimal.

A new method for sparse linear bandits reduces exploration-exploitation tradeoff.

problem Sparse linear bandits in high-dimensional settings with finite actions.
method Best subset selection for parameter estimation and doubly growing epochs for regret minimization.
result Achieves nearly dimension-independent regret of ildeO(sT) ilde{\mathcal{O}}(s\sqrt{T}) with high probability.

Algorithm reduces regret in misspecified linear contextual bandits.

problem Misspecified linear contextual bandits with bounded misspecification.
method Data selection scheme for online regression, leveraging uncertainty.
result Regret bound of O~(d2/Δ)\tilde O(d^2/Δ) when ζO~(Δ/d)ζ \leq \tilde O(Δ/\sqrt{d}).