Optimal Statistical Rates for Decentralised Non-Parametric Regression with Linear Speed-Up

We analyse the learning performance of Distributed Gradient Descent in the context of multi-agent decentralised non-parametric regression with the square loss function when i.i.d. samples are assigned to agents. We show that if agents hold sufficiently many samples with respect to the network size, then Distributed Gradient Descent achieves optimal statistical rates with a number of iterations that scales, up to a threshold, with the inverse of the spectral gap of the gossip matrix divided by the number of samples owned by each agent raised to a problem-dependent power. The presence of the threshold comes from statistics. It encodes the existence of a "big data" regime where the number of required iterations does not depend on the network topology. In this regime, Distributed Gradient Descent achieves optimal statistical rates with the same order of iterations as gradient descent run with all the samples in the network. Provided the communication delay is sufficiently small, the distributed protocol yields a linear speed-up in runtime compared to the single-machine protocol. This is in contrast to decentralised optimisation algorithms that do not exploit statistics and only yield a linear speed-up in graphs where the spectral gap is bounded away from zero. Our results exploit the statistical concentration of quantities held by agents and shed new light on the interplay between statistics and communication in decentralised methods. Bounds are given in the standard non-parametric setting with source/capacity assumptions

A Deep Recurrent Q Network Towards Self-adapting Distributed Microservices Architecture (in press)

One desired aspect of microservices architecture is the ability to self-adapt its own architecture and behaviour in response to changes in the operational environment. To achieve the desired high levels of self-adaptability, this research implements the distributed microservices architectures model, as informed by the MAPE-K model. The proposed architecture employs a multi adaptation agents supported by a centralised controller, that can observe the environment and execute a suitable adaptation action. The adaptation planning is managed by a deep recurrent Q-network (DRQN). It is argued that such integration between DRQN and MDP agents in a MAPE-K model offers distributed microservice architecture with self-adaptability and high levels of availability and scalability. Integrating DRQN into the adaptation process improves the effectiveness of the adaptation and reduces any adaptation risks, including resources over-provisioning and thrashing. The performance of DRQN is evaluated against deep Q-learning and policy gradient algorithms including: i) deep q-network (DQN), ii) dulling deep Q-network (DDQN), iii) a policy gradient neural network (PGNN), and iv) deep deterministic policy gradient (DDPG). The DRQN implementation in this paper manages to outperform the above mentioned algorithms in terms of total reward, less adaptation time, lower error rates, plus faster convergence and training times. We strongly believe that DRQN is more suitable for driving the adaptation in distributed services-oriented architecture and offers better performance than other dynamic decision-making algorithms

Random Neural Networks and Optimisation

In this thesis we introduce new models and learning algorithms for the Random Neural Network (RNN), and we develop RNN-based and other approaches for the solution of emergency management optimisation problems. With respect to RNN developments, two novel supervised learning algorithms are proposed. The first, is a gradient descent algorithm for an RNN extension model that we have introduced, the RNN with synchronised interactions (RNNSI), which was inspired from the synchronised firing activity observed in brain neural circuits. The second algorithm is based on modelling the signal-flow equations in RNN as a nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory quasi-Newton algorithm specifically designed for the RNN case. Regarding the investigation of emergency management optimisation problems, we examine combinatorial assignment problems that require fast, distributed and close to optimal solution, under information uncertainty. We consider three different problems with the above characteristics associated with the assignment of emergency units to incidents with injured civilians (AEUI), the assignment of assets to tasks under execution uncertainty (ATAU), and the deployment of a robotic network to establish communication with trapped civilians (DRNCTC). AEUI is solved by training an RNN tool with instances of the optimisation problem and then using the trained RNN for decision making; training is achieved using the developed learning algorithms. For the solution of ATAU problem, we introduce two different approaches. The first is based on mapping parameters of the optimisation problem to RNN parameters, and the second on solving a sequence of minimum cost flow problems on appropriately constructed networks with estimated arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer linear programming formulation, which is based on network flows. Finally, we design and implement distributed heuristic algorithms for the deployment of robots when the civilian locations are known or uncertain