Cognitive Medium Access: Exploration, Exploitation and Competition

This paper establishes the equivalence between cognitive medium access and the competitive multi-armed bandit problem. First, the scenario in which a single cognitive user wishes to opportunistically exploit the availability of empty frequency bands in the spectrum with multiple bands is considered. In this scenario, the availability probability of each channel is unknown to the cognitive user a priori. Hence efficient medium access strategies must strike a balance between exploring the availability of other free channels and exploiting the opportunities identified thus far. By adopting a Bayesian approach for this classical bandit problem, the optimal medium access strategy is derived and its underlying recursive structure is illustrated via examples. To avoid the prohibitive computational complexity of the optimal strategy, a low complexity asymptotically optimal strategy is developed. The proposed strategy does not require any prior statistical knowledge about the traffic pattern on the different channels. Next, the multi-cognitive user scenario is considered and low complexity medium access protocols, which strike the optimal balance between exploration and exploitation in such competitive environments, are developed. Finally, this formalism is extended to the case in which each cognitive user is capable of sensing and using multiple channels simultaneously.Comment: Submitted to IEEE/ACM Trans. on Networking, 14 pages, 2 figure

PAC-Bayesian Analysis of the Exploration-Exploitation Trade-off

We develop a coherent framework for integrative simultaneous analysis of the exploration-exploitation and model order selection trade-offs. We improve over our preceding results on the same subject (Seldin et al., 2011) by combining PAC-Bayesian analysis with Bernstein-type inequality for martingales. Such a combination is also of independent interest for studies of multiple simultaneously evolving martingales.Comment: On-line Trading of Exploration and Exploitation 2 - ICML-2011 workshop. http://explo.cs.ucl.ac.uk/workshop

Superior Exploration-Exploitation Balance with Quantum-Inspired Hadamard Walks

This paper extends the analogies employed in the development of quantum-inspired evolutionary algorithms by proposing quantum-inspired Hadamard walks, called QHW. A novel quantum-inspired evolutionary algorithm, called HQEA, for solving combinatorial optimization problems, is also proposed. The novelty of HQEA lies in it's incorporation of QHW Remote Search and QHW Local Search - the quantum equivalents of classical mutation and local search, that this paper defines. The intuitive reasoning behind this approach, and the exploration-exploitation balance thus occurring is explained. From the results of the experiments carried out on the 0,1-knapsack problem, HQEA performs significantly better than a conventional genetic algorithm, CGA, and two quantum-inspired evolutionary algorithms - QEA and NQEA, in terms of convergence speed and accuracy.Comment: 2 pages, 2 figures, 1 table, late-breakin

Better safe than sorry: Risky function exploitation through safe optimization

Exploration-exploitation of functions, that is learning and optimizing a mapping between inputs and expected outputs, is ubiquitous to many real world situations. These situations sometimes require us to avoid certain outcomes at all cost, for example because they are poisonous, harmful, or otherwise dangerous. We test participants' behavior in scenarios in which they have to find the optimum of a function while at the same time avoid outputs below a certain threshold. In two experiments, we find that Safe-Optimization, a Gaussian Process-based exploration-exploitation algorithm, describes participants' behavior well and that participants seem to care firstly whether a point is safe and then try to pick the optimal point from all such safe points. This means that their trade-off between exploration and exploitation can be seen as an intelligent, approximate, and homeostasis-driven strategy.Comment: 6 pages, submitted to Cognitive Science Conferenc