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Adaptive Design and Refusal Conversions

For me, the idea of adaptive design was influenced by work from the field of clinical trials on multi-stage treatments. Susan Murphy introduced me to adaptive treatment regimes as an approach to the problem. She points to methods developed in the field of reinforcement learning as useful approaches to problems of sequential decisionmaking.

Reinforcement learning describes some policies (i.e. a set of decision rules for a set of sequential decisions) as myopic. A policy is myopic if it only looks at the rewards available at the next step. I'm reading Decision Theory by John Bather right now. He uses an example similar to the following to demonstrate this issue. The following is a simple game. The goal is to get from the yellow square to the green square with the lowest cost. The number in each square is the cost of moving there.Diagonal moves are not allowed.

 

The myopic policy looks only at the next option and goes down a path that ends up with only expensive options to reach the target. The myopic policy is shown in the following picture:

The total cost is 7. The optimal policy looks for the sequence with the lowest cost (since the reward function in this game is to find the lowest cost path). The optimal policy starts out with a a more expensive move, but ends up overall less costly:


I find myself in a similar situation with the telephone experiment that I've been running. It is more efficient in the first step (before refusal conversions). But it is less efficient for refusal conversions. So much so that the overall efficiency is the same for the experimental and control groups.

On the other hand, maybe I can locate a policy for refusal conversions that will be better than either the current experimental or control methods. Even if I'm not able to find such a solution, I still think this is an interesting problem.
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