Scaling Observation-aware Planning in Uncertain Domains

Deciding which sensing capabilities to deploy on an agent in uncertain domains is a fundamental engineering challenge, in which one balances task achievability against the high costs of hardware and processing. This problem has previously been formalized as the Optimal Observability Problem (OOP), based on the well-known Partially Observable Markov Decision Process (POMDP) model for decision-making. This work studies (sub-)symbolic techniques to scale solving of decidable fragments of the OOP, namely the Sensor Selection Problem (SSP) and the Positional Observability Problem (POP). Besides improving the original approach based on parameter synthesis, we develop a new solving method that identifies sensible observation functions via decomposition of POMDPs, improving performance by 3 and 5 orders of magnitude for instance size and runtime, respectively.

What should be observed for optimal reward in POMDPs?

Partially observable Markov Decision Processes (POMDPs) are a standard model for agents making decisions in uncertain environments. Most work on POMDPs focuses on synthesizing strategies based on the available capabilities. However, system designers can often control an agent's observation capabilities, e.g. by placing or selecting sensors. This raises the question of how one should select an agent's sensors cost-effectively such that it achieves the desired goals. In this paper, we study the novel optimal observability problem OOP: Given a POMDP M, how should one change M's observation capabilities within a fixed budget such that its (minimal) expected reward remains below a given threshold? We show that the problem is undecidable in general and decidable when considering positional strategies only. We present two algorithms for a decidable fragment of the OOP: one based on optimal strategies of M's underlying Markov decision process and one based on parameter synthesis with SMT. We report promising results for variants of typical examples from the POMDP literature.