FROST -- Fast row-stochastic optimization with uncoordinated step-sizes

In this paper, we discuss distributed optimization over directed graphs, where doubly-stochastic weights cannot be constructed. Most of the existing algorithms overcome this issue by applying push-sum consensus, which utilizes column-stochastic weights. The formulation of column-stochastic weights requires each agent to know (at least) its out-degree, which may be impractical in e.g., broadcast-based communication protocols. In contrast, we describe FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an optimization algorithm applicable to directed graphs that does not require the knowledge of out-degrees; the implementation of which is straightforward as each agent locally assigns weights to the incoming information and locally chooses a suitable step-size. We show that FROST converges linearly to the optimal solution for smooth and strongly-convex functions given that the largest step-size is positive and sufficiently small.Comment: Submitted for journal publication, currently under revie

Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging

In this paper, we study distributed big-data nonconvex optimization in multi-agent networks. We consider the (constrained) minimization of the sum of a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a convex (possibly) nonsmooth regularizer. Our interest is in big-data problems wherein there is a large number of variables to optimize. If treated by means of standard distributed optimization algorithms, these large-scale problems may be intractable, due to the prohibitive local computation and communication burden at each node. We propose a novel distributed solution method whereby at each iteration agents optimize and then communicate (in an uncoordinated fashion) only a subset of their decision variables. To deal with non-convexity of the cost function, the novel scheme hinges on Successive Convex Approximation (SCA) techniques coupled with i) a tracking mechanism instrumental to locally estimate gradient averages; and ii) a novel block-wise consensus-based protocol to perform local block-averaging operations and gradient tacking. Asymptotic convergence to stationary solutions of the nonconvex problem is established. Finally, numerical results show the effectiveness of the proposed algorithm and highlight how the block dimension impacts on the communication overhead and practical convergence speed

Distributed optimization algorithm for discrete-time heterogeneous multi-agent systems with nonuniform stepsizes

This paper is devoted to the distributed optimization problem of heterogeneous multi-agent systems, where the communication topology is jointly strongly connected and the dynamics of each agent is the first-order or second-order integrator. A new distributed algorithm is first designed for each agent based on the local objective function and the local neighbors' information that each agent can access. By a model transformation, the original closed-loop system is converted into a time-varying system and the system matrix of which is a stochastic matrix at any time. Then, by the properties of the stochastic matrix, it is proven that all agents' position states can converge to the optimal solution of a team objective function provided the union communication topology is strongly connected. Finally, the simulation results are provided to verify the effectiveness of the distributed algorithm proposed in this paper

Adaptive Knobs for Resource Efficient Computing

Performance demands of emerging domains such as artificial intelligence, machine learning and vision, Internet-of-things etc., continue to grow. Meeting such requirements on modern multi/many core systems with higher power densities, fixed power and energy budgets, and thermal constraints exacerbates the run-time management challenge. This leaves an open problem on extracting the required performance within the power and energy limits, while also ensuring thermal safety. Existing architectural solutions including asymmetric and heterogeneous cores and custom acceleration improve performance-per-watt in specific design time and static scenarios. However, satisfying applications’ performance requirements under dynamic and unknown workload scenarios subject to varying system dynamics of power, temperature and energy requires intelligent run-time management. Adaptive strategies are necessary for maximizing resource efficiency, considering i) diverse requirements and characteristics of concurrent applications, ii) dynamic workload variation, iii) core-level heterogeneity and iv) power, thermal and energy constraints. This dissertation proposes such adaptive techniques for efficient run-time resource management to maximize performance within fixed budgets under unknown and dynamic workload scenarios. Resource management strategies proposed in this dissertation comprehensively consider application and workload characteristics and variable effect of power actuation on performance for pro-active and appropriate allocation decisions. Specific contributions include i) run-time mapping approach to improve power budgets for higher throughput, ii) thermal aware performance boosting for efficient utilization of power budget and higher performance, iii) approximation as a run-time knob exploiting accuracy performance trade-offs for maximizing performance under power caps at minimal loss of accuracy and iv) co-ordinated approximation for heterogeneous systems through joint actuation of dynamic approximation and power knobs for performance guarantees with minimal power consumption. The approaches presented in this dissertation focus on adapting existing mapping techniques, performance boosting strategies, software and dynamic approximations to meet the performance requirements, simultaneously considering system constraints. The proposed strategies are compared against relevant state-of-the-art run-time management frameworks to qualitatively evaluate their efficacy