We present more experiments and provide all missing proofs in the appendix. Concretely, Appendix A describes the experiment setup and contains additional numerical experiments. Appendix B and C provide the detailed proofs for our unified privacy guarantee in Theorem 2 and unified utility and communication complexity analysis in Theorem 3, respectively. Appendix D provides the proof for CDP-SGD (Theorem 1). Finally, Appendix E provides the proofs for Section 5, including Lemma 1 (showing that several local gradient estimators satisfy the generic Assumption 3) and Corollaries 1-3 (instantiating Lemma 1 in the unified Theorem 3) for the proposed SoteriaFL-style algorithms.

In distributed optimization and federated learning, asynchronous alternating direction method of multipliers (ADMM) serves as an attractive option for large-scale optimization, data privacy, straggler nodes and variety of objective functions. However, communication costs can become a major bottleneck when the nodes have limited communication budgets or when the data to be communicated is prohibitively large. In this work, we propose introducing coarse quantization to the data to be exchanged in aynchronous ADMM so as to reduce communication overhead for large-scale federated learning and distributed optimization applications. We experimentally verify the convergence of the proposed method for several distributed learning tasks, including neural networks.

Communication compression is a common technique in distributed optimization that can alleviate communication overhead by transmitting compressed gradients and model parameters. However, compression can introduce information distortion, which slows down convergence and incurs more communication rounds to achieve desired solutions. Given the trade-off between lower per-round communication costs and additional rounds of communication, it is unclear whether communication compression reduces the total communication cost. This paper explores the conditions under which unbiased compression, a widely used form of compression, can reduce the total communication cost, as well as the extent to which it can do so. To this end, we present the first theoretical formulation for characterizing the total communication cost in distributed optimization with communication compression. We demonstrate that unbiased compression alone does not necessarily save the total communication cost, but this outcome can be achieved if the compressors used by all workers are further assumed independent. We establish lower bounds on the communication rounds required by algorithms using independent unbiased compressors to minimize smooth convex functions and show that these lower bounds are tight by refining the analysis for ADIANA. Our results reveal that using independent unbiased compression can reduce the total communication cost by a factor of up to $\Theta(\sqrt{\min\{n, \kappa\}})$ when all local smoothness constants are constrained by a common upper bound, where $n$ is the number of workers and $\kappa$ is the condition number of the functions being minimized. These theoretical findings are supported by experimental results.

Federated Learning (FL) plays a prominent role in solving machine learning problems with data distributed across clients. In FL, to reduce the communication overhead of data between clients and the server, each client communicates the local FL parameters instead of the local data. However, when a wireless network connects clients and the server, the communication resource limitations of the clients may prevent completing the training of the FL iterations. Therefore, communication-efficient variants of FL have been widely investigated. Lazily Aggregated Quantized Gradient (LAQ) is one of the promising communication-efficient approaches to lower resource usage in FL. However, LAQ assigns a fixed number of bits for all iterations, which may be communication-inefficient when the number of iterations is medium to high or convergence is approaching. This paper proposes Adaptive Lazily Aggregated Quantized Gradient (A-LAQ), which is a method that significantly extends LAQ by assigning an adaptive number of communication bits during the FL iterations. We train FL in an energy-constraint condition and investigate the convergence analysis for A-LAQ. The experimental results highlight that A-LAQ outperforms LAQ by up to a $50$% reduction in spent communication energy and an $11$% increase in test accuracy.

Federated averaging (FedAvg) is a communication efficient algorithm for the distributed training with an enormous number of clients. In FedAvg, clients keep their data locally for privacy protection; a central parameter server is used to communicate between clients. This central server distributes the parameters to each client and collects the updated parameters from clients. FedAvg is mostly studied in centralized fashions, which requires massive communication between server and clients in each communication. Moreover, attacking the central server can break the whole system's privacy. In this paper, we study the decentralized FedAvg with momentum (DFedAvgM), which is implemented on clients that are connected by an undirected graph. In DFedAvgM, all clients perform stochastic gradient descent with momentum and communicate with their neighbors only. To further reduce the communication cost, we also consider the quantized DFedAvgM. We prove convergence of the (quantized) DFedAvgM under trivial assumptions; the convergence rate can be improved when the loss function satisfies the P{\L} property. Finally, we numerically verify the efficacy of DFedAvgM.

Online advertising allows advertisers to implement fine-tuned targeting of users. While such precise targeting leads to more effective advertising,  it introduces challenging multidimensional pricing and bidding problems for publishers and advertisers. In this context, advertisers and publishers need to deal with an exponential number of possibilities. As a result, designing efficient and compact multidimensional bidding and pricing systems and algorithms are practically important for online advertisement.  Compact bidding languages have already been studied in the context of multiplicative bidding.  In this paper, we study the compact pricing problem.