5,849 research outputs found
Probabilistic Planning via Heuristic Forward Search and Weighted Model Counting
We present a new algorithm for probabilistic planning with no observability.
Our algorithm, called Probabilistic-FF, extends the heuristic forward-search
machinery of Conformant-FF to problems with probabilistic uncertainty about
both the initial state and action effects. Specifically, Probabilistic-FF
combines Conformant-FFs techniques with a powerful machinery for weighted model
counting in (weighted) CNFs, serving to elegantly define both the search space
and the heuristic function. Our evaluation of Probabilistic-FF shows its fine
scalability in a range of probabilistic domains, constituting a several orders
of magnitude improvement over previous results in this area. We use a
problematic case to point out the main open issue to be addressed by further
research
Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting
Weighted model counting (WMC) has emerged as a prevalent approach for
probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF
counting (weighted #DNF) is a special case, where approximations with
probabilistic guarantees are obtained in O(nm), where n denotes the number of
variables, and m the number of clauses of the input DNF, but this is not
scalable in practice. In this paper, we propose a neural model counting
approach for weighted #DNF that combines approximate model counting with deep
learning, and accurately approximates model counts in linear time when width is
bounded. We conduct experiments to validate our method, and show that our model
learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on
Artificial Intelligence (AAAI-20). Code and data available at:
https://github.com/ralphabb/NeuralDNF
ADDMC: Weighted Model Counting with Algebraic Decision Diagrams
We present an algorithm to compute exact literal-weighted model counts of
Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic
programming and uses Algebraic Decision Diagrams as the primary data structure.
We implement this technique in ADDMC, a new model counter. We empirically
evaluate various heuristics that can be used with ADDMC. We then compare ADDMC
to state-of-the-art exact weighted model counters (Cachet, c2d, d4, and
miniC2D) on 1914 standard model counting benchmarks and show that ADDMC
significantly improves the virtual best solver.Comment: Presented at AAAI 202
Pond-Hindsight: Applying Hindsight Optimization to Partially-Observable Markov Decision Processes
Partially-observable Markov decision processes (POMDPs) are especially good at modeling real-world problems because they allow for sensor and effector uncertainty. Unfortunately, such uncertainty makes solving a POMDP computationally challenging. Traditional approaches, which are based on value iteration, can be slow because they find optimal actions for every possible situation. With the help of the Fast Forward (FF) planner, FF- Replan and FF-Hindsight have shown success in quickly solving fully-observable Markov decision processes (MDPs) by solving classical planning translations of the problem. This thesis extends the concept of problem determination to POMDPs by sampling action observations (similar to how FF-Replan samples action outcomes) and guiding the construction of policy trajectories with a conformant (as opposed to classical) planning heuristic. The resultant planner is called POND-Hindsight
Distribution-Aware Sampling and Weighted Model Counting for SAT
Given a CNF formula and a weight for each assignment of values to variables,
two natural problems are weighted model counting and distribution-aware
sampling of satisfying assignments. Both problems have a wide variety of
important applications. Due to the inherent complexity of the exact versions of
the problems, interest has focused on solving them approximately. Prior work in
this area scaled only to small problems in practice, or failed to provide
strong theoretical guarantees, or employed a computationally-expensive maximum
a posteriori probability (MAP) oracle that assumes prior knowledge of a
factored representation of the weight distribution. We present a novel approach
that works with a black-box oracle for weights of assignments and requires only
an {\NP}-oracle (in practice, a SAT-solver) to solve both the counting and
sampling problems. Our approach works under mild assumptions on the
distribution of weights of satisfying assignments, provides strong theoretical
guarantees, and scales to problems involving several thousand variables. We
also show that the assumptions can be significantly relaxed while improving
computational efficiency if a factored representation of the weights is known.Comment: This is a full version of AAAI 2014 pape
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