We describe tradeoffs between the performance in visual decision problems and the control authority that the agent can exercise on the sensing process. We focus on problems of “coverage” (ensuring that all regions in the scene are seen) and “change estimation” (finding and learning an unknown object in an otherwise known and static scene), propose a measure of control authority and empirically relate it to the expected risk and its proxy (conditional entropy of the posterior density). We then show that a “passive” agent can provide no guarantees on performance beyond what is afforded by the priors, and that an “omnipotent” agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically).
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