70 research outputs found
BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization
Despite the success of neural-based combinatorial optimization methods for
end-to-end heuristic learning, out-of-distribution generalization remains a
challenge. In this paper, we present a novel formulation of Combinatorial
Optimization Problems (COPs) as Markov Decision Processes (MDPs) that
effectively leverages common symmetries of COPs to improve out-of-distribution
robustness. Starting from a direct MDP formulation of a constructive method, we
introduce a generic way to reduce the state space, based on Bisimulation
Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize
the bisimulation and show how the reduced state exploits the symmetries of
these problems and facilitates MDP solving. Our approach is principled and we
prove that an optimal policy for the proposed BQ-MDP actually solves the
associated COPs. We illustrate our approach on five classical problems: the
Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing,
Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce
a simple attention-based policy network for the BQ-MDPs, which we train by
imitation of (near) optimal solutions of small instances from a single
distribution. We obtain new state-of-the-art results for the five COPs on both
synthetic and realistic benchmarks. Notably, in contrast to most existing
neural approaches, our learned policies show excellent generalization
performance to much larger instances than seen during training, without any
additional search procedure
Cut elimination in multifocused linear logic
We study cut elimination for a multifocused variant of full linear logic in
the sequent calculus. The multifocused normal form of proofs yields problems
that do not appear in a standard focused system, related to the constraints in
grouping rule instances in focusing phases. We show that cut elimination can be
performed in a sensible way even though the proof requires some specific lemmas
to deal with multifocusing phases, and discuss the difficulties arising with
cut elimination when considering normal forms of proofs in linear logic.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441
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Proceedings of the 13th annual conference of INEBRIA
CITATION: Watson, R., et al. 2016. Proceedings of the 13th annual conference of INEBRIA. Addiction Science & Clinical Practice, 11:13, doi:10.1186/s13722-016-0062-9.The original publication is available at https://ascpjournal.biomedcentral.comENGLISH SUMMARY : Meeting abstracts.https://ascpjournal.biomedcentral.com/articles/10.1186/s13722-016-0062-9Publisher's versio
Logic Programming with Focusing Proofs in Linear Logic
The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is Computation = Proof search
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