Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the result of each test reveals the number of defective items in the tested group. The minimum number of tests achievable by nested test plans was established by Aigner and Schughart in 1985 within a minimax framework. The optimal nested test plan offering this performance, however, was not obtained. In this work, we establish the optimal nested test plan in closed form. This optimal nested test plan is also order optimal among all test plans as the population size approaches infinity. Using heavy-hitter detection as a case study, we show via simulation examples orders of magnitude improvement of the group testing approach over two prevailing sampling-based approaches in detection accuracy and counter consumption. Other applications include anomaly detection and wideband spectrum sensing in cognitive radio systems

Code Construction and Decoding Algorithms for Semi-Quantitative Group Testing with Nonuniform Thresholds

We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the most general semi-quantitative group testing model, we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds. The sequences represent extensions and generalizations of Bh and certain types of super-increasing and lexicographically ordered sequences, and they lead to code structures amenable for efficient recursive decoding. We describe the decoding methods and provide an accompanying computational complexity and performance analysis

Finding a state in a haystack

We consider the problem to single out a particular state among $2^n$ orthogonal pure states. As it turns out, in general the optimal strategy is not to measure the particles separately, but to consider joint properties of the $n$-particle system. The required number of propositions is $n$. There exist $2^n!$ equivalent operational procedures to do so. We enumerate some configurations for three particles, in particular the Greenberger-Horne-Zeilinger (GHZ)- and W-states, which are specific cases of a unitary transformation For the GHZ-case, an explicit physical meaning of the projection operators is discussed.Comment: 11 page

Non-Pickwickian Belief and 'the Gettier Problem'

That in Gettier's alleged counterexamples to the traditional analysis of knowledge as justified true belief the belief condition is satisfied has rarely been questioned. Yet there is reason to doubt that a rational person would come to believe what Gettier's protagonists are said to believe in the way they are said to have come to believe it. If they would not, the examples are not counter-examples to the traditional analysis. I go on to discuss a number of examples inspired by Gettier's and argue that they, too, fail to be counter-examples either for reasons similar to those I have urged or because it is not clear that their subject does not know

Opportunities for financing sustainable development using complementary local currencies

Financing building retrofit projects that contribute to climate change mitigation has always represented a significant barrier. With 28% of global emissions coming from existing buildings, it is of paramount importance to carry out retrofit measures that lead to significant reduction of these emissions. Whilst this is perfectly possible to achieve with current methods and current technology, there is no sufficient conventional finance to carry out zero carbon retrofit at scale required for climate change mitigation. The article introduces an alternative and sustainable business model that creates new opportunities for financing zero carbon retrofit of buildings. It demonstrates that the value of solar energy falling on roofs of buildings can become a driver for new local economic systems, and discusses the requirements for practical application.Peer reviewedFinal Published versio

Learning with Opponent-Learning Awareness

Multi-agent settings are quickly gathering importance in machine learning. This includes a plethora of recent work on deep multi-agent reinforcement learning, but also can be extended to hierarchical RL, generative adversarial networks and decentralised optimisation. In all these settings the presence of multiple learning agents renders the training problem non-stationary and often leads to unstable training or undesired final results. We present Learning with Opponent-Learning Awareness (LOLA), a method in which each agent shapes the anticipated learning of the other agents in the environment. The LOLA learning rule includes a term that accounts for the impact of one agent's policy on the anticipated parameter update of the other agents. Results show that the encounter of two LOLA agents leads to the emergence of tit-for-tat and therefore cooperation in the iterated prisoners' dilemma, while independent learning does not. In this domain, LOLA also receives higher payouts compared to a naive learner, and is robust against exploitation by higher order gradient-based methods. Applied to repeated matching pennies, LOLA agents converge to the Nash equilibrium. In a round robin tournament we show that LOLA agents successfully shape the learning of a range of multi-agent learning algorithms from literature, resulting in the highest average returns on the IPD. We also show that the LOLA update rule can be efficiently calculated using an extension of the policy gradient estimator, making the method suitable for model-free RL. The method thus scales to large parameter and input spaces and nonlinear function approximators. We apply LOLA to a grid world task with an embedded social dilemma using recurrent policies and opponent modelling. By explicitly considering the learning of the other agent, LOLA agents learn to cooperate out of self-interest. The code is at github.com/alshedivat/lola