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An Index-based Deterministic Asymptotically Optimal Algorithm for Constrained Multi-armed Bandit Problems | | Hyeong Soo Chang
; | | Date: |
29 Jul 2020 | | Abstract: | For the model of constrained multi-armed bandit, we show that by construction
there exists an index-based deterministic asymptotically optimal algorithm. The
optimality is achieved by the convergence of the probability of choosing an
optimal feasible arm to one over infinite horizon. The algorithm is built upon
Locatelli et al.’s "anytime parameter-free thresholding" algorithm under the
assumption that the optimal value is known. We provide a finite-time bound to
the probability of the asymptotic optimality given as 1-O(|A|Te^{-T}) where T
is the horizon size and A is the set of the arms in the bandit. We then study a
relaxed-version of the algorithm in a general form that estimates the optimal
value and discuss the asymptotic optimality of the algorithm after a
sufficiently large T with examples. | | Source: | arXiv, 2007.14550 | | Services: | Forum | Review | PDF | Favorites | |
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