QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM

This paper focuses on online kernel learning over a decentralized network. Each agent in the network receives continuous streaming data locally and works collaboratively to learn a nonlinear prediction function that is globally optimal in the reproducing kernel Hilbert space with respect to the total instantaneous costs of all agents. In order to circumvent the curse of dimensionality issue in traditional online kernel learning, we utilize random feature (RF) mapping to convert the non-parametric kernel learning problem into a fixed-length parametric one in the RF space. We then propose a novel learning framework named Online Decentralized Kernel learning via Linearized ADMM (ODKLA) to efficiently solve the online decentralized kernel learning problem. To further improve the communication efficiency, we add the quantization and censoring strategies in the communication stage and develop the Quantized and Communication-censored ODKLA (QC-ODKLA) algorithm. We theoretically prove that both ODKLA and QC-ODKLA can achieve the optimal sublinear regret $\mathcal{O}(\sqrt{T})$ over $T$ time slots. Through numerical experiments, we evaluate the learning effectiveness, communication, and computation efficiencies of the proposed methods

Mobilizing Personalized Federated Learning in Infrastructure-Less and Heterogeneous Environments via Random Walk Stochastic ADMM

This paper explores the challenges of implementing Federated Learning (FL) in practical scenarios featuring isolated nodes with data heterogeneity, which can only be connected to the server through wireless links in an infrastructure-less environment. To overcome these challenges, we propose a novel mobilizing personalized FL approach, which aims to facilitate mobility and resilience. Specifically, we develop a novel optimization algorithm called Random Walk Stochastic Alternating Direction Method of Multipliers (RWSADMM). RWSADMM capitalizes on the server's random movement toward clients and formulates local proximity among their adjacent clients based on hard inequality constraints rather than requiring consensus updates or introducing bias via regularization methods. To mitigate the computational burden on the clients, an efficient stochastic solver of the approximated optimization problem is designed in RWSADMM, which provably converges to the stationary point almost surely in expectation. Our theoretical and empirical results demonstrate the provable fast convergence and substantial accuracy improvements achieved by RWSADMM compared to baseline methods, along with its benefits of reduced communication costs and enhanced scalability.Comment: 28 pages, 7 figures, 3 tables, 1 algorithm. Proof details are provided in the main body of the pape

Energy Sharing Models for Renewable Energy Integration: Subtransmission Level, Distribution Level, and Community Level

Distributed energy resources (DERs) are being embedded rapidly and widely in the power grid and promoting the transformation of the centralized power industry to a more deregulated mode. However, how to safely and efficiently consume renewable energy is becoming a major concern. In this regard, energy sharing at both grid-scale and community-scale has emerged as a new solution to encourage participants to actively bid instead of acting as price takers and has the potential to accelerate the integration of DERs and decrease energy costs. At the grid level, two risk-averse energy sharing models are developed to safely integrate renewable energy by considering the network constraints and overbidding risk. A risk-averse two-stage stochastic game model is proposed for the regional energy sharing market (ESM). The sample average approximation (SAA) method is used to approximate the stochastic Cournot-Nash equilibrium. In addition, a data-driven joint chance-constrained game is developed for energy sharing in the local energy market (LEM). This model considers the maximum outputs of renewable energy aggregators (REAs) are random variables whose probability distributions are unknown, but the decision-maker has access to finite samples. Case studies show that the proposed game models can effectively increase the profit of reliable players and decrease the overbidding risk. At the community level, a community server enables energy sharing among users based on the Bayesian game-based pricing mechanism. It can also control the community energy storage system (CESS) to smooth the load based on the grid's price signal. A communication-censored ADMM for sharing problems is developed to decrease the communication cost between the community and the grid. Moreover, a co-optimization model for the plan and operation of the shared CESS is developed. By introducing the price uncertainty and degradation cost, the proposed model could more accurately evaluate the performance of the CESS and tap more economic potential. This thesis provides proof of the Nash equilibrium of all game models and the convergence of all market clearing algorithms. The proposed models and methods present performance improvement compared with existing solutions. The work in this thesis indicates that energy sharing is possible to implement at different levels of the power system and could benefit the participants and promote the integration of DERs

Efficient inference algorithms for network activities

The real social network and associated communities are often hidden under the declared friend or group lists in social networks. We usually observe the manifestation of these hidden networks and communities in the form of recurrent and time-stamped individuals' activities in the social network. The inference of relationship between users/nodes or groups of users/nodes could be further complicated when activities are interval-censored, that is, when one only observed the number of activities that occurred in certain time windows. The same phenomenon happens in the online advertisement world where the advertisers often offer a set of advertisement impressions and observe a set of conversions (i.e. product/service adoption). In this case, the advertisers desire to know which advertisements best appeal to the customers and most importantly, their rate of conversions. Inspired by these challenges, we investigated inference algorithms that efficiently recover user relationships in both cases: time-stamped data and interval-censored data. In case of time-stamped data, we proposed a novel algorithm called NetCodec, which relies on a Hawkes process that models the intertwine relationship between group participation and between-user influence. Using Bayesian variational principle and optimization techniques, NetCodec could infer both group participation and user influence simultaneously with iteration complexity being O((N+I)G), where N is the number of events, I is the number of users, and G is the number of groups. In case of interval-censored data, we proposed a Monte-Carlo EM inference algorithm where we iteratively impute the time-stamped events using a Poisson process that has intensity function approximates the underlying intensity function. We show that that proposed simulated approach delivers better inference performance than baseline methods. In the advertisement problem, we propose a Click-to-Conversion delay model that uses Hawkes processes to model the advertisement impressions and thinned Poisson processes to model the Click-to-Conversion mechanism. We then derive an efficient Maximum Likelihood Estimator which utilizes the Minorization-Maximization framework. We verify the model against real life online advertisement logs in comparison with recent conversion rate estimation methods. To facilitate reproducible research, we also developed an open-source software package that focuses on various Hawkes processes proposed in the above mentioned works and prior works. We provided efficient parallel (multi-core) implementations of the inference algorithms using the Bayesian variational inference framework. To further speed up these inference algorithms, we also explored distributed optimization techniques for convex optimization under the distributed data situation. We formulate this problem as a consensus-constrained optimization problem and solve it with the alternating direction method for multipliers (ADMM). It turns out that using bipartite graph as communication topology exhibits the fastest convergence.Ph.D

Exact Diffusion Learning over Networks

In this dissertation, we study optimization, adaptation, and learning problems over connected networks. In these problems, each agent $k$ collects and learns from its own local data and is able to communicate with its local neighbors. While each single node in the network may not be capable of sophisticated behavior on its own, the agents collaborate to solve large-scale and challenging learning problems. Different approaches have been proposed in the literature to boost the learning capabilities of networked agents. Among these approaches, the class of diffusion strategies has been shown to be particularly well-suited due to their enhanced stability range over other methods and improved performance in adaptive scenarios. However, diffusion implementations suffer from a small inherent bias in the iterates. When a constant step-size is employed to solve deterministic optimization problems, the iterates generated by the diffusion strategy will converge to a small neighborhood around the desired global solution but not to the exact solution itself. This bias is not due to any gradient noise arising from stochastic approximation; it is instead due to the update structure in diffusion implementations. The existence of the bias leads to three questions: (1) What is the origin of this inherent bias? (2) Can it be eliminated? (3) Does the correction of the bias bring benefits to distributed optimization, distributed adaptation, or distributed learning?This dissertation provides affirmative solutions to these questions. Specifically, we design a new {\em exact diffusion} approach that eliminates the inherent bias in diffusion. Exact diffusion has almost the same structure as diffusion, with the addition of a ``correction'' step between the adaptation and combination steps. Next, this dissertation studies the performance of exact diffusion for the scenarios of distributed optimization, distributed adaptation, and distributed learning, respectively. For distributed optimization, exact diffusion is proven to converge exponentially fast to the {\em exact} global solution under proper conditions. For distributed adaptation, exact diffusion is proven to have better steady-state mean-square-error than diffusion, and this superiority is analytically shown to be more evident for sparsely-connected networks such as line, cycle, grid, and other topologies. In distributed learning, exact diffusion can be integrated with the amortized variance-reduced gradient method (AVRG) so that it converges exponentially fast to the exact global solution while employing stochastic gradients per iteration. This dissertation also compares exact diffusion with other state-of-the-art methods in literature. Intensive numerical simulations are provided to illustrate the theoretical results derived in the dissertation