45,405 research outputs found
Greed Is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation
The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel ϵ-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that ϵ-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g. EI and UCB), particularly with a limited budget. In higher dimensions ϵ-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution
Interactive Submodular Set Cover
We introduce a natural generalization of submodular set cover and exact
active learning with a finite hypothesis class (query learning). We call this
new problem interactive submodular set cover. Applications include advertising
in social networks with hidden information. We give an approximation guarantee
for a novel greedy algorithm and give a hardness of approximation result which
matches up to constant factors. We also discuss negative results for simpler
approaches and present encouraging early experimental results.Comment: 15 pages, 1 figur
Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs
Crowdsourcing platforms are now extensively used for conducting subjective
pairwise comparison studies. In this setting, a pairwise comparison dataset is
typically gathered via random sampling, either \emph{with} or \emph{without}
replacement. In this paper, we use tools from random graph theory to analyze
these two random sampling methods for the HodgeRank estimator. Using the
Fiedler value of the graph as a measurement for estimator stability
(informativeness), we provide a new estimate of the Fiedler value for these two
random graph models. In the asymptotic limit as the number of vertices tends to
infinity, we prove the validity of the estimate. Based on our findings, for a
small number of items to be compared, we recommend a two-stage sampling
strategy where a greedy sampling method is used initially and random sampling
\emph{without} replacement is used in the second stage. When a large number of
items is to be compared, we recommend random sampling with replacement as this
is computationally inexpensive and trivially parallelizable. Experiments on
synthetic and real-world datasets support our analysis
Multimodal Hierarchical Dirichlet Process-based Active Perception
In this paper, we propose an active perception method for recognizing object
categories based on the multimodal hierarchical Dirichlet process (MHDP). The
MHDP enables a robot to form object categories using multimodal information,
e.g., visual, auditory, and haptic information, which can be observed by
performing actions on an object. However, performing many actions on a target
object requires a long time. In a real-time scenario, i.e., when the time is
limited, the robot has to determine the set of actions that is most effective
for recognizing a target object. We propose an MHDP-based active perception
method that uses the information gain (IG) maximization criterion and lazy
greedy algorithm. We show that the IG maximization criterion is optimal in the
sense that the criterion is equivalent to a minimization of the expected
Kullback--Leibler divergence between a final recognition state and the
recognition state after the next set of actions. However, a straightforward
calculation of IG is practically impossible. Therefore, we derive an efficient
Monte Carlo approximation method for IG by making use of a property of the
MHDP. We also show that the IG has submodular and non-decreasing properties as
a set function because of the structure of the graphical model of the MHDP.
Therefore, the IG maximization problem is reduced to a submodular maximization
problem. This means that greedy and lazy greedy algorithms are effective and
have a theoretical justification for their performance. We conducted an
experiment using an upper-torso humanoid robot and a second one using synthetic
data. The experimental results show that the method enables the robot to select
a set of actions that allow it to recognize target objects quickly and
accurately. The results support our theoretical outcomes.Comment: submitte
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