54,237 research outputs found
Adaptive sampling strategies for risk-averse stochastic optimization with constraints
We introduce adaptive sampling methods for risk-neutral and risk-averse
stochastic programs with deterministic constraints. In particular, we propose a
variant of the stochastic projected gradient method where the sample size used
to approximate the reduced gradient is determined a posteriori and updated
adaptively. We also propose an SQP-type method based on similar adaptive
sampling principles. Both methods lead to a significant reduction in cost.
Numerical experiments from finance and engineering illustrate the performance
and efficacy of the presented algorithms. The methods here are applicable to a
broad class of expectation-based risk measures, however, we focus mainly on
expected risk and conditional value-at-risk minimization problems
Bayesian Optimization for Adaptive MCMC
This paper proposes a new randomized strategy for adaptive MCMC using
Bayesian optimization. This approach applies to non-differentiable objective
functions and trades off exploration and exploitation to reduce the number of
potentially costly objective function evaluations. We demonstrate the strategy
in the complex setting of sampling from constrained, discrete and densely
connected probabilistic graphical models where, for each variation of the
problem, one needs to adjust the parameters of the proposal mechanism
automatically to ensure efficient mixing of the Markov chains.Comment: This paper contains 12 pages and 6 figures. A similar version of this
paper has been submitted to AISTATS 2012 and is currently under revie
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Sequential Design for Ranking Response Surfaces
We propose and analyze sequential design methods for the problem of ranking
several response surfaces. Namely, given response surfaces over a
continuous input space , the aim is to efficiently find the index of
the minimal response across the entire . The response surfaces are not
known and have to be noisily sampled one-at-a-time. This setting is motivated
by stochastic control applications and requires joint experimental design both
in space and response-index dimensions. To generate sequential design
heuristics we investigate stepwise uncertainty reduction approaches, as well as
sampling based on posterior classification complexity. We also make connections
between our continuous-input formulation and the discrete framework of pure
regret in multi-armed bandits. To model the response surfaces we utilize
kriging surrogates. Several numerical examples using both synthetic data and an
epidemics control problem are provided to illustrate our approach and the
efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
Faster Coordinate Descent via Adaptive Importance Sampling
Coordinate descent methods employ random partial updates of decision
variables in order to solve huge-scale convex optimization problems. In this
work, we introduce new adaptive rules for the random selection of their
updates. By adaptive, we mean that our selection rules are based on the dual
residual or the primal-dual gap estimates and can change at each iteration. We
theoretically characterize the performance of our selection rules and
demonstrate improvements over the state-of-the-art, and extend our theory and
algorithms to general convex objectives. Numerical evidence with hinge-loss
support vector machines and Lasso confirm that the practice follows the theory.Comment: appearing at AISTATS 201
Block-Randomized Gradient Descent Methods with Importance Sampling for CP Tensor Decomposition
This work considers the problem of computing the CANDECOMP/PARAFAC (CP)
decomposition of large tensors. One popular way is to translate the problem
into a sequence of overdetermined least squares subproblems with Khatri-Rao
product (KRP) structure. In this work, for tensor with different levels of
importance in each fiber, combining stochastic optimization with randomized
sampling, we present a mini-batch stochastic gradient descent algorithm with
importance sampling for those special least squares subproblems. Four different
sampling strategies are provided. They can avoid forming the full KRP or
corresponding probabilities and sample the desired fibers from the original
tensor directly. Moreover, a more practical algorithm with adaptive step size
is also given. For the proposed algorithms, we present their convergence
properties and numerical performance. The results on synthetic data show that
our algorithms outperform the existing algorithms in terms of accuracy or the
number of iterations
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