Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks

We study nonconvex distributed optimization in multiagent networks where the communications between nodes is modeled as a time-varying sequence of arbitrary digraphs. We introduce a novel broadcast-based distributed algorithmic framework for the (constrained) minimization of the sum of a smooth (possibly nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on Successive Convex Approximation (SCA) techniques coupled with i) a tracking mechanism instrumental to locally estimate the gradients of agents' cost functions; and ii) a novel broadcast protocol to disseminate information and distribute the computation among the agents. Asymptotic convergence to stationary solutions is established. A key feature of the proposed algorithm is that it neither requires the double-stochasticity of the consensus matrices (but only column stochasticity) nor the knowledge of the graph sequence to implement. To the best of our knowledge, the proposed framework is the first broadcast-based distributed algorithm for convex and nonconvex constrained optimization over arbitrary, time-varying digraphs. Numerical results show that our algorithm outperforms current schemes on both convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA, US

Fair Knapsack

We study the following multiagent variant of the knapsack problem. We are given a set of items, a set of voters, and a value of the budget; each item is endowed with a cost and each voter assigns to each item a certain value. The goal is to select a subset of items with the total cost not exceeding the budget, in a way that is consistent with the voters' preferences. Since the preferences of the voters over the items can vary significantly, we need a way of aggregating these preferences, in order to select the socially best valid knapsack. We study three approaches to aggregating voters' preferences, which are motivated by the literature on multiwinner elections and fair allocation. This way we introduce the concepts of individually best, diverse, and fair knapsack. We study the computational complexity (including parameterized complexity, and complexity under restricted domains) of the aforementioned multiagent variants of knapsack.Comment: Extended abstract will appear in Proc. of 33rd AAAI 201

An incremental approach to genetic algorithms based classification

Incremental learning has been widely addressed in the machine learning literature to cope with learning tasks where the learning environment is ever changing or training samples become available over time. However, most research work explores incremental learning with statistical algorithms or neural networks, rather than evolutionary algorithms. The work in this paper employs genetic algorithms (GAs) as basic learning algorithms for incremental learning within one or more classifier agents in a multi-agent environment. Four new approaches with different initialization schemes are proposed. They keep the old solutions and use an “integration” operation to integrate them with new elements to accommodate new attributes, while biased mutation and crossover operations are adopted to further evolve a reinforced solution. The simulation results on benchmark classification data sets show that the proposed approaches can deal with the arrival of new input attributes and integrate them with the original input space. It is also shown that the proposed approaches can be successfully used for incremental learning and improve classification rates as compared to the retraining GA. Possible applications for continuous incremental training and feature selection are also discussed

Smart Microgrids: Overview and Outlook

The idea of changing our energy system from a hierarchical design into a set of nearly independent microgrids becomes feasible with the availability of small renewable energy generators. The smart microgrid concept comes with several challenges in research and engineering targeting load balancing, pricing, consumer integration and home automation. In this paper we first provide an overview on these challenges and present approaches that target the problems identified. While there exist promising algorithms for the particular field, we see a missing integration which specifically targets smart microgrids. Therefore, we propose an architecture that integrates the presented approaches and defines interfaces between the identified components such as generators, storage, smart and \dq{dumb} devices.Comment: presented at the GI Informatik 2012, Braunschweig Germany, Smart Grid Worksho

Incremental multiple objective genetic algorithms

This paper presents a new genetic algorithm approach to multi-objective optimization problemsIncremental Multiple Objective Genetic Algorithms (IMOGA). Different from conventional MOGA methods, it takes each objective into consideration incrementally. The whole evolution is divided into as many phases as the number of objectives, and one more objective is considered in each phase. Each phase is composed of two stages: first, an independent population is evolved to optimize one specific objective; second, the better-performing individuals from the evolved single-objective population and the multi-objective population evolved in the last phase are joined together by the operation of integration. The resulting population then becomes an initial multi-objective population, to which a multi-objective evolution based on the incremented objective set is applied. The experiment results show that, in most problems, the performance of IMOGA is better than that of three other MOGAs, NSGA-II, SPEA and PAES. IMOGA can find more solutions during the same time span, and the quality of solutions is better

Computing large market equilibria using abstractions

Computing market equilibria is an important practical problem for market design (e.g. fair division, item allocation). However, computing equilibria requires large amounts of information (e.g. all valuations for all buyers for all items) and compute power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: 1) filling in unknown valuations using techniques from matrix completion, 2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions