118 research outputs found
The Complexity of Reasoning with FODD and GFODD
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a
knowledge representation that is useful in mechanizing decision theoretic
planning in relational domains. GFODDs generalize function-free first order
logic and include numerical values and numerical generalizations of existential
and universal quantification. Previous work presented heuristic inference
algorithms for GFODDs and implemented these heuristics in systems for decision
theoretic planning. In this paper, we study the complexity of the computational
problems addressed by such implementations. In particular, we study the
evaluation problem, the satisfiability problem, and the equivalence problem for
GFODDs under the assumption that the size of the intended model is given with
the problem, a restriction that guarantees decidability. Our results provide a
complete characterization placing these problems within the polynomial
hierarchy. The same characterization applies to the corresponding restriction
of problems in first order logic, giving an interesting new avenue for
efficient inference when the number of objects is bounded. Our results show
that for formulas, and for corresponding GFODDs, evaluation and
satisfiability are complete, and equivalence is
complete. For formulas evaluation is complete, satisfiability
is one level higher and is complete, and equivalence is
complete.Comment: A short version of this paper appears in AAAI 2014. Version 2
includes a reorganization and some expanded proof
Adaptive Robotic Information Gathering via Non-Stationary Gaussian Processes
Robotic Information Gathering (RIG) is a foundational research topic that
answers how a robot (team) collects informative data to efficiently build an
accurate model of an unknown target function under robot embodiment
constraints. RIG has many applications, including but not limited to autonomous
exploration and mapping, 3D reconstruction or inspection, search and rescue,
and environmental monitoring. A RIG system relies on a probabilistic model's
prediction uncertainty to identify critical areas for informative data
collection. Gaussian Processes (GPs) with stationary kernels have been widely
adopted for spatial modeling. However, real-world spatial data is typically
non-stationary -- different locations do not have the same degree of
variability. As a result, the prediction uncertainty does not accurately reveal
prediction error, limiting the success of RIG algorithms. We propose a family
of non-stationary kernels named Attentive Kernel (AK), which is simple, robust,
and can extend any existing kernel to a non-stationary one. We evaluate the new
kernel in elevation mapping tasks, where AK provides better accuracy and
uncertainty quantification over the commonly used stationary kernels and the
leading non-stationary kernels. The improved uncertainty quantification guides
the downstream informative planner to collect more valuable data around the
high-error area, further increasing prediction accuracy. A field experiment
demonstrates that the proposed method can guide an Autonomous Surface Vehicle
(ASV) to prioritize data collection in locations with significant spatial
variations, enabling the model to characterize salient environmental features.Comment: International Journal of Robotics Research (IJRR). arXiv admin note:
text overlap with arXiv:2205.0642
Stochastic Planning with Lifted Symbolic Trajectory Optimization
This paper investigates online stochastic planning for problems with large factored state and action spaces. One promising approach in recent work estimates the quality of applicable actions in the current state through aggregate simulation from the states they reach. This leads to significant speedup, compared to search over concrete states and actions, and suffices to guide decision making in cases where the performance of a random policy is informative of the quality of a state. The paper makes two significant improvements to this approach. The first, taking inspiration from lifted belief propagation, exploits the structure of the problem to derive a more compact computation graph for aggregate simulation. The second improvement replaces the random policy embedded in the computation graph with symbolic variables that are optimized simultaneously with the search for high quality actions. This expands the scope of the approach to problems that require deep search and where information is lost quickly with random steps. An empirical evaluation shows that these ideas significantly improve performance, leading to state of the art performance on hard planning problems
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Reasoning with Models
We develop a model-based approach to reasoning, in which the knowledge base is represented as a set of models (satisfying assignments) rather then a logical formula, and the set of queries is restricted. We show that for every propositional knowledge base (KB) there exists a set of characteristic models with the property that a query is true in KB if and only if it is satisfied by the models in this set. We fully characterize a set of theories for which the model-based representation is compact and provides efficient reasoning. These include cases where the formula-based representation does not support efficient reasoning. In addition, we consider the model-based approach to abductive reasoning and show that for any propositional KB, reasoning with its model-based representation yields an abductive explanation in time that is polynomial in its size. Some of our technical results make use of the Monotone Theory, a new characterization of Boolean functions introduced in [Bsh93]. The notion of restricted queries is inherent to our approach. This is a wide class of queries for which reasoning is very efficient and exact, even when the model-based representation KB provides only an approximate representation of the "world". Moreover, we show that the theory developed here generalizes the model-based approach to reasoning with Horn theories [KKS93], and captures even the notion of reasoning with Horn-approximations [SK91]. Our result characterizes the Horn theories for which the approach suggested in [KKS93] is useful and the phenomena observed there, regarding the relative sizes of the formula-based representation and model-based representation of KB is explained and put in a wider context.Engineering and Applied Science
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