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We extend a relaxation technique due to Bertsimas and Nino-Mora for therestless bandit problem to the case where arbitrary costs penalize switchingbetween the bandits. We also construct a one-step lookahead policy using thesolution of the relaxation. Computational experiments and a bound forapproximate dynamic programming provide some empirical support for theheuristic.

A Linear Programming Relaxation and a Heuristic for the Restless Bandit Problem with General Switching Costs