Federated Averaging (FedAvg, also known as Local-SGD) (McMahan et al., 2017) is a classical federated learning algorithm in which clients run multiple local SGD steps before communicating their update to an orchestrating server. We propose a new federated learning algorithm, FedPAGE, able to further reduce the communication complexity by utilizing the recent optimal PAGE method (Li et al., 2021) instead of plain SGD in FedAvg. We show that FedPAGE uses much fewer communication rounds than previous local methods for both federated convex and nonconvex optimization. Concretely, 1) in the convex setting, the number of communication rounds of FedPAGE is $O(\frac{N^{3/4}}{S\epsilon})$, improving the best-known result $O(\frac{N}{S\epsilon})$ of SCAFFOLD (Karimireddy et al.,2020) by a factor of $N^{1/4}$, where $N$ is the total number of clients (usually is very large in federated learning), $S$ is the sampled subset of clients in each communication round, and $\epsilon$ is the target error; 2) in the nonconvex setting, the number of communication rounds of FedPAGE is $O(\frac{\sqrt{N}+S}{S\epsilon^2})$, improving the best-known result $O(\frac{N^{2/3}}{S^{2/3}\epsilon^2})$ of SCAFFOLD (Karimireddy et al.,2020) by a factor of $N^{1/6}S^{1/3}$, if the sampled clients $S\leq \sqrt{N}$. Note that in both settings, the communication cost for each round is the same for both FedPAGE and SCAFFOLD. As a result, FedPAGE achieves new state-of-the-art results in terms of communication complexity for both federated convex and nonconvex optimization.
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Federated learning (FL) is a privacy-preserving paradigm where multiple participants jointly solve a machine learning problem without sharing raw data. Unlike traditional distributed learning, a unique characteristic of FL is statistical heterogeneity, namely, data distributions across participants are different from each other. Meanwhile, recent advances in the interpretation of neural networks have seen a wide use of neural tangent kernel (NTK) for convergence and generalization analyses. In this paper, we propose a novel FL paradigm empowered by the NTK framework. The proposed paradigm addresses the challenge of statistical heterogeneity by transmitting update data that are more expressive than those of the traditional FL paradigms. Specifically, sample-wise Jacobian matrices, rather than model weights/gradients, are uploaded by participants. The server then constructs an empirical kernel matrix to update a global model without explicitly performing gradient descent. We further develop a variant with improved communication efficiency and enhanced privacy. Numerical results show that the proposed paradigm can achieve the same accuracy while reducing the number of communication rounds by an order of magnitude compared to federated averaging.
We propose and analyze a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization, where each machine can calculate stochastic gradients of the same population objective, as well as stochastic Hessian-vector products (products of an independent unbiased estimator of the Hessian of the population objective with arbitrary vectors), with many such stochastic computations performed between rounds of communication. We show that our method can reduce the number, and frequency, of required communication rounds compared to existing methods without hurting performance, by proving convergence guarantees for quasi-self-concordant objectives (e.g., logistic regression), alongside empirical evidence.
We develop a model selection approach to tackle reinforcement learning with adversarial corruption in both transition and reward. For finite-horizon tabular MDPs, without prior knowledge on the total amount of corruption, our algorithm achieves a regret bound of $\widetilde{\mathcal{O}}(\min\{\frac{1}{\Delta}, \sqrt{T}\}+C)$ where $T$ is the number of episodes, $C$ is the total amount of corruption, and $\Delta$ is the reward gap between the best and the second-best policy. This is the first worst-case optimal bound achieved without knowledge of $C$, improving previous results of Lykouris et al. (2021); Chen et al. (2021); Wu et al. (2021). For finite-horizon linear MDPs, we develop a computationally efficient algorithm with a regret bound of $\widetilde{\mathcal{O}}(\sqrt{(1+C)T})$, and another computationally inefficient one with $\widetilde{\mathcal{O}}(\sqrt{T}+C)$, improving the result of Lykouris et al. (2021) and answering an open question by Zhang et al. (2021b). Finally, our model selection framework can be easily applied to other settings including linear bandits, linear contextual bandits, and MDPs with general function approximation, leading to several improved or new results.
We study the MARINA method of Gorbunov et al (2021) -- the current state-of-the-art distributed non-convex optimization method in terms of theoretical communication complexity. Theoretical superiority of this method can be largely attributed to two sources: the use of a carefully engineered biased stochastic gradient estimator, which leads to a reduction in the number of communication rounds, and the reliance on {\em independent} stochastic communication compression operators, which leads to a reduction in the number of transmitted bits within each communication round. In this paper we i) extend the theory of MARINA to support a much wider class of potentially {\em correlated} compressors, extending the reach of the method beyond the classical independent compressors setting, ii) show that a new quantity, for which we coin the name {\em Hessian variance}, allows us to significantly refine the original analysis of MARINA without any additional assumptions, and iii) identify a special class of correlated compressors based on the idea of {\em random permutations}, for which we coin the term Perm$K$, the use of which leads to $O(\sqrt{n})$ (resp. $O(1 + d/\sqrt{n})$) improvement in the theoretical communication complexity of MARINA in the low Hessian variance regime when $d\geq n$ (resp. $d \leq n$), where $n$ is the number of workers and $d$ is the number of parameters describing the model we are learning. We corroborate our theoretical results with carefully engineered synthetic experiments with minimizing the average of nonconvex quadratics, and on autoencoder training with the MNIST dataset.
In federated learning (FL), a machine learning model is trained on multiple nodes in a decentralized manner, while keeping the data local and not shared with other nodes. However, FL requires the nodes to also send information on the model parameters to a central server for aggregation. However, the information sent from the nodes to the server may reveal some details about each node's local data, thus raising privacy concerns. Furthermore, the repetitive uplink transmission from the nodes to the server may result in a communication overhead and network congestion. To address these two challenges, in this paper, a novel two-bit aggregation algorithm is proposed with guaranteed differential privacy and reduced uplink communication overhead. Extensive experiments demonstrate that the proposed aggregation algorithm can achieve the same performance as state-of-the-art approaches on datasets such as MNIST, Fashion MNIST, CIFAR-10, and CIFAR-100, while ensuring differential privacy and improving communication efficiency.
Federated Learning Networks (FLNs) have been envisaged as a promising paradigm to collaboratively train models among mobile devices without exposing their local privacy data. Due to the need for frequent model updates and communications, FLNs are vulnerable to various attacks (e.g., eavesdropping attacks, inference attacks, poisoning attacks, and backdoor attacks). Balancing privacy protection with efficient distributed model training is a key challenge for FLNs. Existing countermeasures incur high computation costs and are only designed for specific attacks on FLNs. In this paper, we bridge this gap by proposing the Covert Communication-based Federated Learning (CCFL) approach. Based on the emerging communication security technique of covert communication which hides the existence of wireless communication activities, CCFL can degrade attackers' capability of extracting useful information from the FLN training protocol, which is a fundamental step for most existing attacks, and thereby holistically enhances the privacy of FLNs. We experimentally evaluate CCFL extensively under real-world settings in which the FL latency is optimized under given security requirements. Numerical results demonstrate the significant effectiveness of the proposed approach in terms of both training efficiency and communication security.
Fairness has emerged as a critical problem in federated learning (FL). In this work, we identify a cause of unfairness in FL -- \emph{conflicting} gradients with large differences in the magnitudes. To address this issue, we propose the federated fair averaging (FedFV) algorithm to mitigate potential conflicts among clients before averaging their gradients. We first use the cosine similarity to detect gradient conflicts, and then iteratively eliminate such conflicts by modifying both the direction and the magnitude of the gradients. We further show the theoretical foundation of FedFV to mitigate the issue conflicting gradients and converge to Pareto stationary solutions. Extensive experiments on a suite of federated datasets confirm that FedFV compares favorably against state-of-the-art methods in terms of fairness, accuracy and efficiency.
We consider the exploration-exploitation trade-off in reinforcement learning and we show that an agent imbued with a risk-seeking utility function is able to explore efficiently, as measured by regret. The parameter that controls how risk-seeking the agent is can be optimized exactly, or annealed according to a schedule. We call the resulting algorithm K-learning and show that the corresponding K-values are optimistic for the expected Q-values at each state-action pair. The K-values induce a natural Boltzmann exploration policy for which the `temperature' parameter is equal to the risk-seeking parameter. This policy achieves an expected regret bound of $\tilde O(L^{3/2} \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the total number of elapsed time-steps. This bound is only a factor of $L$ larger than the established lower bound. K-learning can be interpreted as mirror descent in the policy space, and it is similar to other well-known methods in the literature, including Q-learning, soft-Q-learning, and maximum entropy policy gradient, and is closely related to optimism and count based exploration methods. K-learning is simple to implement, as it only requires adding a bonus to the reward at each state-action and then solving a Bellman equation. We conclude with a numerical example demonstrating that K-learning is competitive with other state-of-the-art algorithms in practice.
In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.
This work considers the problem of provably optimal reinforcement learning for episodic finite horizon MDPs, i.e. how an agent learns to maximize his/her long term reward in an uncertain environment. The main contribution is in providing a novel algorithm --- Variance-reduced Upper Confidence Q-learning (vUCQ) --- which enjoys a regret bound of $\widetilde{O}(\sqrt{HSAT} + H^5SA)$, where the $T$ is the number of time steps the agent acts in the MDP, $S$ is the number of states, $A$ is the number of actions, and $H$ is the (episodic) horizon time. This is the first regret bound that is both sub-linear in the model size and asymptotically optimal. The algorithm is sub-linear in that the time to achieve $\epsilon$-average regret for any constant $\epsilon$ is $O(SA)$, which is a number of samples that is far less than that required to learn any non-trivial estimate of the transition model (the transition model is specified by $O(S^2A)$ parameters). The importance of sub-linear algorithms is largely the motivation for algorithms such as $Q$-learning and other "model free" approaches. vUCQ algorithm also enjoys minimax optimal regret in the long run, matching the $\Omega(\sqrt{HSAT})$ lower bound. Variance-reduced Upper Confidence Q-learning (vUCQ) is a successive refinement method in which the algorithm reduces the variance in $Q$-value estimates and couples this estimation scheme with an upper confidence based algorithm. Technically, the coupling of both of these techniques is what leads to the algorithm enjoying both the sub-linear regret property and the asymptotically optimal regret.
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