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Excerpt from Conservation Laws, Extended Polymatroids and Multi-Armed Bandit Problems: An Unified Approach to Indexable Systems
An interesting distinction, which is not emphasized in the literature, is that examples (1) and (2) above are indexable systems, but they are not in general decomposable systems. Example however, has a more refined structure. It is indexable, but not decomposable. Under discounting, while it is decomposable under the average cost criterion (the cit. Rule). As already observed, the multi-armed bandit problem is an example of a decomposable system, while example (4) above is also decomposable.
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