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Although perception is an increasingly dominant portion of the overallcomputational cost for autonomous systems, only a fraction of the informationperceived is likely to be relevant to the current task. To alleviate theseperception costs, we develop a novel simultaneous perception-action designframework wherein an agent senses only the task-relevant information. Thisformulation differs from that of a partially observable Markov decisionprocess, since the agent is free to synthesize not only its policy for actionselection but also its belief-dependent observation function. The methodenables the agent to balance its perception costs with those incurred byoperating in its environment. To obtain a computationally tractable solution,we approximate the value function using a novel method of invariant finitebelief sets, wherein the agent acts exclusively on a finite subset of thecontinuous belief space. We solve the approximate problem through valueiteration in which a linear program is solved individually for each beliefstate in the set, in each iteration. Finally, we prove that the valuefunctions, under an assumption on their structure, converge to their continuousstate-space values as the sample density increases.

Simultaneous Perception-Action Design via Invariant Finite Belief Sets