703 research outputs found
Portfolio Allocation for Bayesian Optimization
Bayesian optimization with Gaussian processes has become an increasingly
popular tool in the machine learning community. It is efficient and can be used
when very little is known about the objective function, making it popular in
expensive black-box optimization scenarios. It uses Bayesian methods to sample
the objective efficiently using an acquisition function which incorporates the
model's estimate of the objective and the uncertainty at any given point.
However, there are several different parameterized acquisition functions in the
literature, and it is often unclear which one to use. Instead of using a single
acquisition function, we adopt a portfolio of acquisition functions governed by
an online multi-armed bandit strategy. We propose several portfolio strategies,
the best of which we call GP-Hedge, and show that this method outperforms the
best individual acquisition function. We also provide a theoretical bound on
the algorithm's performance.Comment: This revision contains an updated the performance bound and other
minor text change
Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
We propose a novel information-theoretic approach for Bayesian optimization
called Predictive Entropy Search (PES). At each iteration, PES selects the next
evaluation point that maximizes the expected information gained with respect to
the global maximum. PES codifies this intractable acquisition function in terms
of the expected reduction in the differential entropy of the predictive
distribution. This reformulation allows PES to obtain approximations that are
both more accurate and efficient than other alternatives such as Entropy Search
(ES). Furthermore, PES can easily perform a fully Bayesian treatment of the
model hyperparameters while ES cannot. We evaluate PES in both synthetic and
real-world applications, including optimization problems in machine learning,
finance, biotechnology, and robotics. We show that the increased accuracy of
PES leads to significant gains in optimization performance
An Entropy Search Portfolio for Bayesian Optimization
Bayesian optimization is a sample-efficient method for black-box global
optimization. How- ever, the performance of a Bayesian optimization method very
much depends on its exploration strategy, i.e. the choice of acquisition
function, and it is not clear a priori which choice will result in superior
performance. While portfolio methods provide an effective, principled way of
combining a collection of acquisition functions, they are often based on
measures of past performance which can be misleading. To address this issue, we
introduce the Entropy Search Portfolio (ESP): a novel approach to portfolio
construction which is motivated by information theoretic considerations. We
show that ESP outperforms existing portfolio methods on several real and
synthetic problems, including geostatistical datasets and simulated control
tasks. We not only show that ESP is able to offer performance as good as the
best, but unknown, acquisition function, but surprisingly it often gives better
performance. Finally, over a wide range of conditions we find that ESP is
robust to the inclusion of poor acquisition functions.Comment: 10 pages, 5 figure
Decoding Guilty Minds
A central tenet of Anglo-American penal law is that in order for an actor to be found criminally liable, a proscribed act must be accompanied by a guilty mind. While it is easy to understand the importance of this principle in theory, in practice it requires jurors and judges to decide what a person was thinking months or years earlier at the time of the alleged offense, either about the results of his conduct or about some elemental fact (such as whether the briefcase he is carrying contains drugs). Despite the central importance of this task in the administration of criminal justice, there has been very little research investigating how people go about making these decisions, and how these decisions relate to their intuitions about culpability. Understanding the cognitive mechanisms that govern this task is important for the law, not only to explore the possibility of systemic biases and errors in attributions of culpability but also to probe the intuitions that underlie them.
In a set of six exploratory studies reported here, we examine the way in which individuals infer othersâ legally relevant mental states about elemental facts, using the framework established over fifty years ago by the Model Penal Code (âMPCâ). The widely adopted MPC framework delineates and defines the four now-familiar culpable mental states: purpose, knowledge, recklessness, and negligence. Our studies reveal that with little to no training, jury-eligible Americans can apply the MPC framework in a manner that is largely congruent with the basic assumptions of the MPCâs mental state hierarchy. However, our results also indicate that subjectsâ intuitions about the level of culpability warranting criminal punishment diverge significantly from prevailing legal practice; subjects tend to regard recklessness as a sufficient basis for punishment under circumstances where the legislatures and courts tend to require knowledge
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