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Two-stage index computation for bandits with switching penalties I : switching costs

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  • Jose Nino-Mora

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    Abstract

    This paper addresses the multi-armed bandit problem with switching costs. Asawa and Teneketzis (1996) introduced an index that partly characterizes optimal policies, attaching to each bandit state a "continuation index" (its Gittins index) and a "switching index". They proposed to jointly compute both as the Gittins index of a bandit having 2n states — when the original bandit has n states — which results in an eight-fold increase in O($n^{3}$) arithmetic operations relative to those to compute the continuation index alone. This paper presents a more efficient, decoupled computation method, which in a first stage computes the continuation index and then, in a second stage, computes the switching index an order of magnitude faster in at most $n^{2}$+O(n) arithmetic operations. The paper exploits the fact that the Asawa and Teneketzis index is the Whittle, or marginal productivity, index of a classic bandit with switching costs in its restless reformulation, by deploying work-reward analysis and PCL-indexability methods introduced by the author. A computational study demonstrates the dramatic runtime savings achieved by the new algorithm, the near-optimality of the index policy, and its substantial gains against the benchmark Gittins index policy across a wide range of instances.

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws074109.

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    Date of creation: May 2007
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    Handle: RePEc:cte:wsrepe:ws074109

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