22 research outputs found
Towards Incremental Cylindrical Algebraic Decomposition in Maple
Cylindrical Algebraic Decomposition (CAD) is an important tool within
computational real algebraic geometry, capable of solving many problems for
polynomial systems over the reals. It has long been studied by the Symbolic
Computation community and has found recent interest in the Satisfiability
Checking community. The present report describes a proof of concept
implementation of an Incremental CAD algorithm in Maple, where CADs are built
and then refined as additional polynomial constraints are added. The aim is to
make CAD suitable for use as a theory solver for SMT tools who search for
solutions by continually reformulating logical formula and querying whether a
logical solution is admissible. We describe experiments for the proof of
concept, which clearly display the computational advantages compared to
iterated re-computation. In addition, the project implemented this work under
the recently verified Lazard projection scheme (with corresponding Lazard
valuation).Comment: FLoC 2018. arXiv admin note: substantial text overlap with
arXiv:1804.0856
Neural Variational Inference For Estimating Uncertainty in Knowledge Graph Embeddings
Recent advances in Neural Variational Inference allowed for a renaissance in
latent variable models in a variety of domains involving high-dimensional data.
While traditional variational methods derive an analytical approximation for
the intractable distribution over the latent variables, here we construct an
inference network conditioned on the symbolic representation of entities and
relation types in the Knowledge Graph, to provide the variational
distributions. The new framework results in a highly-scalable method. Under a
Bernoulli sampling framework, we provide an alternative justification for
commonly used techniques in large-scale stochastic variational inference, which
drastically reduce training time at a cost of an additional approximation to
the variational lower bound. We introduce two models from this highly scalable
probabilistic framework, namely the Latent Information and Latent Fact models,
for reasoning over knowledge graph-based representations. Our Latent
Information and Latent Fact models improve upon baseline performance under
certain conditions. We use the learnt embedding variance to estimate predictive
uncertainty during link prediction, and discuss the quality of these learnt
uncertainty estimates. Our source code and datasets are publicly available
online at
https://github.com/alexanderimanicowenrivers/Neural-Variational-Knowledge-Graphs.Comment: Accepted at IJCAI 19 Neural-Symbolic Learning and Reasoning Worksho
Are we Forgetting about Compositional Optimisers in Bayesian Optimisation?
Bayesian optimisation presents a sample-efficient methodology for global optimisation. Within this framework, a crucial performance-determining subroutine is the maximisation of the acquisition function, a task complicated by the fact that acquisition functions tend to be non-convex and thus nontrivial to optimise. In this paper, we undertake a comprehensive empirical study of approaches to maximise the acquisition function. Additionally, by deriving novel, yet mathematically equivalent, compositional forms for popular acquisition functions, we recast the maximisation task as a compositional optimisation problem, allowing us to benefit from the extensive literature in this field. We highlight the empirical advantages of the compositional approach to acquisition function maximisation across 3958 individual experiments comprising synthetic optimisation tasks as well as tasks from Bayesmark. Given the generality of the acquisition function maximisation subroutine, we posit that the adoption of compositional optimisers has the potential to yield performance improvements across all domains in which Bayesian optimisation is currently being applied. An open-source implementation is made available at https://github.com/huawei-noah/noah-research/tree/CompBO/BO/HEBO/CompBO
Sauté RL: Almost Surely Safe Reinforcement Learning Using State Augmentation
Satisfying safety constraints almost surely (or with probability one) can be critical for the deployment of Reinforcement Learning (RL) in real-life applications. For example, plane landing and take-off should ideally occur with probability one. We address the problem by introducing Safety Augmented (Saute) Markov Decision Processes (MDPs), where the safety constraints are eliminated by augmenting them into the state-space and reshaping the objective. We show that Saute MDP satisfies the Bellman equation and moves us closer to solving Safe RL with constraints satisfied almost surely. We argue that Saute MDP allows viewing the Safe RL problem from a different perspective enabling new features. For instance, our approach has a plug-and-play nature, i.e., any RL algorithm can be "Sauteed”. Additionally, state augmentation allows for policy generalization across safety constraints. We finally show that Saute RL algorithms can outperform their state-of-the-art counterparts when constraint satisfaction is of high importance