arXiv subjects

M. T. Hale

Publications and source records attributed to M. T. Hale.

3 recordsLinked to original sources

arXiv2020

A Decentralized Multi-Objective Optimization Algorithm

During the past two decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions. However, this formulation implies a decision regarding the relative importance of each objective function. In fact, optimizing the sum is a special case of a multi-objective problem in which all objectives are prioritized equally. In this paper, a distributed optimization algorithm that explores Pareto optimal solutions for non-homogeneously weighted sums of objective functions is proposed. This exploration is performed through a new rule based on agents' priorities that generates edge weights in agents' communication graph. These weights determine how agents update their decision variables with information received from other agents in the network. Agents initially disagree on the priorities of the objective functions though they are driven to agree upon them as they optimize. As a result, agents still reach a common solution. The network-level weight matrix is (non-doubly) stochastic, which contrasts with many works on the subject in which it is doubly-stochastic. New theoretical analyses are therefore developed to ensure convergence of the proposed algorithm. This paper provides a gradient-based optimization algorithm, proof of convergence to solutions, and convergence rates of the proposed algorithm. It is shown that agents' initial priorities influence the convergence rate of the proposed algorithm and that these initial choices affect its long-run behavior. Numerical results performed with different numbers of agents illustrate the performance and efficiency of the proposed algorithm.

cs.MA↗

arXiv2016

Approximately Truthful Multi-Agent Optimization Using Cloud-Enforced Joint Differential Privacy

Multi-agent coordination problems often require agents to exchange state information in order to reach some collective goal, such as agreement on a final state value. In some cases, it is feasible that opportunistic agents may deceptively report false state values for their own benefit, e.g., to claim a larger portion of shared resources. Motivated by such cases, this paper presents a multi-agent coordination framework which disincentivizes opportunistic misreporting of state information. This paper focuses on multi-agent coordination problems that can be stated as nonlinear programs, with non-separable constraints coupling the agents. In this setting, an opportunistic agent may be tempted to skew the problem's constraints in its favor to reduce its local cost, and this is exactly the behavior we seek to disincentivize. The framework presented uses a primal-dual approach wherein the agents compute primal updates and a centralized cloud computer computes dual updates. All computations performed by the cloud are carried out in a way that enforces joint differential privacy, which adds noise in order to dilute any agent's influence upon the value of its cost function in the problem. We show that this dilution deters agents from intentionally misreporting their states to the cloud, and present bounds on the possible cost reduction an agent can attain through misreporting its state. This work extends our earlier work on incorporating ordinary differential privacy into multi-agent optimization, and we show that this work can be modified to provide a disincentivize for misreporting states to the cloud. Numerical results are presented to demonstrate convergence of the optimization algorithm under joint differential privacy.

math.OC↗

arXiv2016

Hamiltonian-Based Algorithm for Optimal Control

This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed controls and projects the final result into the space of ordinary controls. It is based on the descent direction from a given relaxed control towards a pointwise minimizer of the Hamiltonian. This direction comprises a form of gradient projection and for some systems, is argued to have computational advantages over direct gradient directions. The algorithm is shown to be applicable to a class of hybrid optimal control problems. The theoretical results, concerning convergence of the algorithm, are corroborated by simulation examples on switched-mode hybrid systems as well as on a problem of balancing transmission- and motion energy in a mobile robotic system.

math.OC↗