39 research outputs found
XOR-Sampling for Network Design with Correlated Stochastic Events
Many network optimization problems can be formulated as stochastic network
design problems in which edges are present or absent stochastically.
Furthermore, protective actions can guarantee that edges will remain present.
We consider the problem of finding the optimal protection strategy under a
budget limit in order to maximize some connectivity measurements of the
network. Previous approaches rely on the assumption that edges are independent.
In this paper, we consider a more realistic setting where multiple edges are
not independent due to natural disasters or regional events that make the
states of multiple edges stochastically correlated. We use Markov Random Fields
to model the correlation and define a new stochastic network design framework.
We provide a novel algorithm based on Sample Average Approximation (SAA)
coupled with a Gibbs or XOR sampler. The experimental results on real road
network data show that the policies produced by SAA with the XOR sampler have
higher quality and lower variance compared to SAA with Gibbs sampler.Comment: In Proceedings of the Twenty-sixth International Joint Conference on
Artificial Intelligence (IJCAI-17). The first two authors contribute equall
Efficient Learning of PDEs via Taylor Expansion and Sparse Decomposition into Value and Fourier Domains
Accelerating the learning of Partial Differential Equations (PDEs) from
experimental data will speed up the pace of scientific discovery. Previous
randomized algorithms exploit sparsity in PDE updates for acceleration. However
such methods are applicable to a limited class of decomposable PDEs, which have
sparse features in the value domain. We propose Reel, which accelerates the
learning of PDEs via random projection and has much broader applicability. Reel
exploits the sparsity by decomposing dense updates into sparse ones in both the
value and frequency domains. This decomposition enables efficient learning when
the source of the updates consists of gradually changing terms across large
areas (sparse in the frequency domain) in addition to a few rapid updates
concentrated in a small set of "interfacial" regions (sparse in the value
domain). Random projection is then applied to compress the sparse signals for
learning. To expand the model applicability, Taylor series expansion is used in
Reel to approximate the nonlinear PDE updates with polynomials in the
decomposable form. Theoretically, we derive a constant factor approximation
between the projected loss function and the original one with poly-logarithmic
number of projected dimensions. Experimentally, we provide empirical evidence
that our proposed Reel can lead to faster learning of PDE models (70-98%
reduction in training time when the data is compressed to 1% of its original
size) with comparable quality as the non-compressed models
Multi-Entity Dependence Learning with Rich Context via Conditional Variational Auto-encoder
Multi-Entity Dependence Learning (MEDL) explores conditional correlations
among multiple entities. The availability of rich contextual information
requires a nimble learning scheme that tightly integrates with deep neural
networks and has the ability to capture correlation structures among
exponentially many outcomes. We propose MEDL_CVAE, which encodes a conditional
multivariate distribution as a generating process. As a result, the variational
lower bound of the joint likelihood can be optimized via a conditional
variational auto-encoder and trained end-to-end on GPUs. Our MEDL_CVAE was
motivated by two real-world applications in computational sustainability: one
studies the spatial correlation among multiple bird species using the eBird
data and the other models multi-dimensional landscape composition and human
footprint in the Amazon rainforest with satellite images. We show that
MEDL_CVAE captures rich dependency structures, scales better than previous
methods, and further improves on the joint likelihood taking advantage of very
large datasets that are beyond the capacity of previous methods.Comment: The first two authors contribute equall
Bootstrap State Representation using Style Transfer for Better Generalization in Deep Reinforcement Learning
Deep Reinforcement Learning (RL) agents often overfit the training
environment, leading to poor generalization performance. In this paper, we
propose Thinker, a bootstrapping method to remove adversarial effects of
confounding features from the observation in an unsupervised way, and thus, it
improves RL agents' generalization. Thinker first clusters experience
trajectories into several clusters. These trajectories are then bootstrapped by
applying a style transfer generator, which translates the trajectories from one
cluster's style to another while maintaining the content of the observations.
The bootstrapped trajectories are then used for policy learning. Thinker has
wide applicability among many RL settings. Experimental results reveal that
Thinker leads to better generalization capability in the Procgen benchmark
environments compared to base algorithms and several data augmentation
techniques.Comment: Accepted at ECML-PKDD 202
Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration With Provable Guarantees
Satisfiability Modulo Counting (SMC) encompasses problems that require both
symbolic decision-making and statistical reasoning. Its general formulation
captures many real-world problems at the intersection of symbolic and
statistical Artificial Intelligence. SMC searches for policy interventions to
control probabilistic outcomes. Solving SMC is challenging because of its
highly intractable nature(-complete), incorporating
statistical inference and symbolic reasoning. Previous research on SMC solving
lacks provable guarantees and/or suffers from sub-optimal empirical
performance, especially when combinatorial constraints are present. We propose
XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly
intractable SMC problems with constant approximation guarantees. XOR-SMC
transforms the highly intractable SMC into satisfiability problems, by
replacing the model counting in SMC with SAT formulae subject to randomized XOR
constraints. Experiments on solving important SMC problems in AI for social
good demonstrate that XOR-SMC finds solutions close to the true optimum,
outperforming several baselines which struggle to find good approximations for
the intractable model counting in SMC
Learning Markov Random Fields for Combinatorial Structures via Sampling through Lov\'asz Local Lemma
Learning to generate complex combinatorial structures satisfying constraints
will have transformative impacts in many application domains. However, it is
beyond the capabilities of existing approaches due to the highly intractable
nature of the embedded probabilistic inference. Prior works spend most of the
training time learning to separate valid from invalid structures but do not
learn the inductive biases of valid structures. We develop NEural Lov\'asz
Sampler (Nelson), which embeds the sampler through Lov\'asz Local Lemma (LLL)
as a fully differentiable neural network layer. Our Nelson-CD embeds this
sampler into the contrastive divergence learning process of Markov random
fields. Nelson allows us to obtain valid samples from the current model
distribution. Contrastive divergence is then applied to separate these samples
from those in the training set. Nelson is implemented as a fully differentiable
neural net, taking advantage of the parallelism of GPUs. Experimental results
on several real-world domains reveal that Nelson learns to generate 100\% valid
structures, while baselines either time out or cannot ensure validity. Nelson
also outperforms other approaches in running time, log-likelihood, and MAP
scores.Comment: accepted by AAAI 2023. The first two authors contribute equall