Control of large distributed systems using games with pure strategy nash equilibria

Control mechanisms for optimisation in large distributed systems cannot be constructed based on traditional methods of control because they are typically characterised by distributed information and costly and/or noisy communication. Furthermore, noisy observations and dynamism are also inherent to these systems, so their control mechanisms need to be flexible, agile and robust in the face of these characteristics. In such settings, a good control mechanism should satisfy the following four design requirements: (i) it should produce high quality solutions, (ii) it should be robustness and flexibility in the face of additions, removals and failures of components, (iii) it should operate by making limited use of communication, and (iv) its operation should be computational feasible. Against this background, in order to satisfy these requirements, in this thesis we adopt a design approach based on dividing control over the system across a team of self–interested agents. Such multi–agent systems (MAS) are naturally distributed (matching the application domains in question), and by pursing their own private goals, the agents can collectively implement robust, flexible and scalable control mechanisms. In more detail, the design approach we adopt is (i) to use games with pure strategy Nash equilibria as a framework or template for constructing the agents’ utility functions, such that good solutions to the optimisation problem arise at the pure strategy Nash equilibria of the game, and (ii) to derive distributed techniques for solving the games for their Nash equilibria. The specific problems we tackle can be grouped into four main topics. First, we investigate a class of local algorithms for distributed constraint optimisation problems (DCOPs). We introduce a unifying analytical framework for studying such algorithms, and develop a parameterisation of the algorithm design space, which represents a mapping from the algorithms’ components to their performance according to each of our design requirements. Second, we develop a game–theoretic control mechanism for distributed dynamic task allocation and scheduling problems. The model in question is an expansion of DCOPs to encompass dynamic problems, and the control mechanism we derive builds on the insights from our first topic to address our four design requirements. Third, we elaborate a general class of problems including DCOPs with noisy rewards and state observations, which are realistic traits of great concern in real–world problems, and derive control mechanisms for these environments. These control mechanism allow the agents to either learn their reward functions or decide when to make observations of the world’s state and/or communicate their beliefs over the state of the world, in such a manner that they perform well according to our design requirements. Fourth, we derive an optimal algorithm for computing and optimising over pure strategy Nash equilibria in games with sparse interaction structure. By exploiting the structure present in many multi-agent interactions, this distributed algorithm can efficiently compute equilibria that optimise various criteria, thus reducing the computational burden on any one agent and operating using less communication than an equivalent centralised algorithms.For each of these topics, the control mechanisms that we derive are developed such that they perform well according to all four f our design requirements. In sum, by making the above contributions to these specific topics, we demonstrate that the general approach of using games with pure strategy Nash equilibria as a template for designing MAS produces good control mechanisms for large distributed systems

A Distributed Algorithm for Demand Response with Mixed-Integer Variables

This letter presents a fast distributed algorithm for aggregating a large number of households with mixed-integer variables and intricate couplings between devices. The proposed fast distributed gradient algorithm is applied to the double smoothed dual function of the adopted DR model. The results also show that, with minimal parameter adjustments, the convergence of the dual objective exhibits the same behavior irrespective of the system size.Comment: 2 pages, 1 figure, to be published in IEEE Transactions on Smart Grid Letter

Convergent learning algorithms for potential games with unknown noisy rewards

In this paper, we address the problem of convergence to Nash equilibria in games with rewards that are initially unknown and which must be estimated over time from noisy observations. These games arise in many real-world applications, whenever rewards for actions cannot be prespecified and must be learned on-line. Standard results in game theory, however, do not consider such settings. Specifically, using results from stochastic approximation and differential inclusions, we prove the convergence of variants of fictitious play and adaptive play to Nash equilibria in potential games and weakly acyclic games, respectively. These variants all use a multi-agent version of Q-learning to estimate the reward functions and a novel form of the e-greedy decision rule to select an action. Furthermore, we derive e-greedy decision rules that exploit the sparse interaction structure encoded in two compact graphical representations of games, known as graphical and hypergraphical normal form, to improve the convergence rate of the learning algorithms. The structure captured in these representations naturally occurs in many distributed optimisation and control applications. Finally, we demonstrate the efficacy of the algorithms in a simulated ad hoc wireless sensor network management problem