Abstract
In this paper, we view a policy or plan as a transition system over a space of information states that reflect a robot’s or other observer’s perspective based on limited sensing, memory, computation, and actuation. Regardless of whether policies are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. Toward the quest to find the best policies, we establish in a general setting that minimal information transition systems (ITSs) exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for feasible policies.
This work was supported by a European Research Council Advanced Grant (ERC AdG, ILLUSIVE: Foundations of Perception Engineering, 101020977), Academy of Finland (projects PERCEPT 322637, CHiMP 342556), and Business Finland (project HUMOR 3656/31/2019).
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Notes
- 1.
We could use the same approach for the external system too. In that case, let \((X, Y \times U, F)\) be this augmented transition system corresponding to the external, in which F is the set of transitions such that \(F =\{ (x, (y,u), x') \in X \times (Y \times U) \times X \mid y=h(x) \wedge x'=f(x,u)\}\). Further creating bipartite graphs (for either system) such that transitions from a state correspond either to an observation \(y\in Y\) or to an action \(u\in U\) allows us to describe the coupling as a form of intersecting two automata. However, because it is not central to this paper we will not elaborate on this topic.
- 2.
A transition system \((S,\varLambda ,T)\) is full, if \(\forall s\in S, \lambda \in \varLambda \) there exists at least one \(s'\in S\) with \((s,\lambda ,s')\in T\).
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Sakcak, B., Weinstein, V., LaValle, S.M. (2023). The Limits of Learning and Planning: Minimal Sufficient Information Transition Systems. In: LaValle, S.M., O’Kane, J.M., Otte, M., Sadigh, D., Tokekar, P. (eds) Algorithmic Foundations of Robotics XV. WAFR 2022. Springer Proceedings in Advanced Robotics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-21090-7_16
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