 Rewarded Bayesian box search Bellman equation

ID: rewarded-bayesian-box-search-bellman-equation

If discovery in box

i

earns reward

R_{i}

and stopping earns zero, the Bellman equation is

V (p) = max {0, max_{i} [- c_{i} + α_{i} p_{i} R_{i} + (1 - α_{i} p_{i}) V (p^{(i)})]} .

\sum_{i} c_{i} / (α_{i} R_{i}) < 1

, every posterior state has some

i

with

α_{i} p_{i} R_{i} > c_{i}

, so stopping is never optimal.

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