A Faster Index Algorithm and a Computational Study for Bandits with Switching Costs

Abstract

We address the intractable multi-armed bandit problem with switching costs, for which an index that partially characterizes optimal policies was introduced (Asawa, M., D. Teneketzis. 1996. Multi-armed bandits with switching penalties. IEEE Trans. Automatic Control 41 328–348), attaching to each project state a “continuation index” (its Gittins index) and a “switching index.” Asawa and Teneketzis proposed to jointly compute both as the Gittins index of a project with 2n states—when the original project has n states—resulting in an eightfold increase in O(n 3 ) arithmetic operations relative to those to compute the continuation index. We present a faster 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, achieving overall a fourfold reduction in arithmetic operations and substantially reduced memory operations. The analysis exploits the fact that the Asawa and Teneketzis index is the marginal productivity index of the project in its restless reformulation, using methods introduced by the author. Extensive computational experiments are reported, which demonstrate the dramatic runtime speedups achieved by the new algorithm, as well as the near optimality of the resultant index policy and its substantial gains against the benchmark Gittins index policy across a wide range of randomly generated two- and three-project instances.

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