61,426 research outputs found
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
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
We present a tutorial on Bayesian optimization, a method of finding the
maximum of expensive cost functions. Bayesian optimization employs the Bayesian
technique of setting a prior over the objective function and combining it with
evidence to get a posterior function. This permits a utility-based selection of
the next observation to make on the objective function, which must take into
account both exploration (sampling from areas of high uncertainty) and
exploitation (sampling areas likely to offer improvement over the current best
observation). We also present two detailed extensions of Bayesian optimization,
with experiments---active user modelling with preferences, and hierarchical
reinforcement learning---and a discussion of the pros and cons of Bayesian
optimization based on our experiences
Planning as Optimization: Dynamically Discovering Optimal Configurations for Runtime Situations
The large number of possible configurations of modern software-based systems,
combined with the large number of possible environmental situations of such
systems, prohibits enumerating all adaptation options at design time and
necessitates planning at run time to dynamically identify an appropriate
configuration for a situation. While numerous planning techniques exist, they
typically assume a detailed state-based model of the system and that the
situations that warrant adaptations are known. Both of these assumptions can be
violated in complex, real-world systems. As a result, adaptation planning must
rely on simple models that capture what can be changed (input parameters) and
observed in the system and environment (output and context parameters). We
therefore propose planning as optimization: the use of optimization strategies
to discover optimal system configurations at runtime for each distinct
situation that is also dynamically identified at runtime. We apply our approach
to CrowdNav, an open-source traffic routing system with the characteristics of
a real-world system. We identify situations via clustering and conduct an
empirical study that compares Bayesian optimization and two types of
evolutionary optimization (NSGA-II and novelty search) in CrowdNav
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
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