Federated learning is a powerful distributed learning scheme that allows numerous edge devices to collaboratively train a model without sharing their data. However, training is resource-intensive for edge devices, and limited network bandwidth is often the main bottleneck. Prior work often overcomes the constraints by condensing the models or messages into compact formats, e.g., by gradient compression or distillation. In contrast, we propose ProgFed, the first progressive training framework for efficient and effective federated learning. It inherently reduces computation and two-way communication costs while maintaining the strong performance of the final models. We theoretically prove that ProgFed converges at the same asymptotic rate as standard training on full models. Extensive results on a broad range of architectures, including CNNs (VGG, ResNet, ConvNets) and U-nets, and diverse tasks from simple classification to medical image segmentation show that our highly effective training approach saves up to $20\%$ computation and up to $63\%$ communication costs for converged models. As our approach is also complimentary to prior work on compression, we can achieve a wide range of trade-offs by combining these techniques, showing reduced communication of up to $50\times$ at only $0.1\%$ loss in utility. Code is available at https://github.com/a514514772/ProgFed.

Traditional federated optimization methods perform poorly with heterogeneous data (i.e.\ , accuracy reduction), especially for highly skewed data. In this paper, we investigate the label distribution skew in FL, where the distribution of labels varies across clients. First, we investigate the label distribution skew from a statistical view. We demonstrate both theoretically and empirically that previous methods based on softmax cross-entropy are not suitable, which can result in local models heavily overfitting to minority classes and missing classes. Additionally, we theoretically introduce a deviation bound to measure the deviation of the gradient after local update. At last, we propose FedLC (\textbf{Fed}erated learning via \textbf{L}ogits \textbf{C}alibration), which calibrates the logits before softmax cross-entropy according to the probability of occurrence of each class. FedLC applies a fine-grained calibrated cross-entropy loss to local update by adding a pairwise label margin. Extensive experiments on federated datasets and real-world datasets demonstrate that FedLC leads to a more accurate global model and much improved performance. Furthermore, integrating other FL methods into our approach can further enhance the performance of the global model.

In this paper, we study the adaptive step size random walk gradient descent with momentum for decentralized optimization, in which the training samples are drawn dependently with each other. We establish theoretical convergence rates of the adaptive step size random walk gradient descent with momentum for both convex and nonconvex settings. In particular, we prove that adaptive random walk algorithms perform as well as the non-adaptive method for dependent data in general cases but achieve acceleration when the stochastic gradients are “sparse”. Moreover, we study the zeroth-order version of adaptive random walk gradient descent and provide corresponding convergence results. All assumptions used in this paper are mild and general, making our results applicable to many machine learning problems.

Fine-tuning models on edge devices like mobile phones would enable privacy-preserving personalization over sensitive data. However, edge training has historically been limited to relatively small models with simple architectures because training is both memory and energy intensive. We present POET, an algorithm to enable training large neural networks on memory-scarce battery-operated edge devices. POET jointly optimizes the integrated search search spaces of rematerialization and paging, two algorithms to reduce the memory consumption of backpropagation. Given a memory budget and a run-time constraint, we formulate a mixed-integer linear program (MILP) for energy-optimal training. Our approach enables training significantly larger models on embedded devices while reducing energy consumption while not modifying mathematical correctness of backpropagation. We demonstrate that it is possible to fine-tune both ResNet-18 and BERT within the memory constraints of a Cortex-M class embedded device while outperforming current edge training methods in energy efficiency. POET is an open-source project available at https://github.com/ShishirPatil/poet

Many areas of deep learning benefit from using increasingly larger neural networks trained on public data, as is the case for pre-trained models for NLP and computer vision. Training such models requires a lot of computational resources (e.g., HPC clusters) that are not available to small research groups and independent researchers. One way to address it is for several smaller groups to pool their computational resources together and train a model that benefits all participants. Unfortunately, in this case, any participant can jeopardize the entire training run by sending incorrect updates, deliberately or by mistake. Training in presence of such peers requires specialized distributed training algorithms with Byzantine tolerance. These algorithms often sacrifice efficiency by introducing redundant communication or passing all updates through a trusted server, making it infeasible to apply them to large-scale deep learning, where models can have billions of parameters. In this work, we propose a novel protocol for secure (Byzantine-tolerant) decentralized training that emphasizes communication efficiency.

Concurrent algorithmic implementations of Stochastic Gradient Descent (SGD) give rise to critical questions for compute-intensive Machine Learning (ML). Asynchrony implies speedup in some contexts, and challenges in others, as stale updates may lead to slower, or non-converging executions. While previous works showed asynchrony-adaptiveness can improve stability and speedup by reducing the step size for stale updates according to static rules, there is no one-size-fits-all adaptation rule, since the optimal strategy depends on several factors. We introduce (i)~$\mathtt{ASAP.SGD}$, an analytical framework capturing necessary and desired properties of staleness-adaptive step size functions and (ii)~\textsc{tail}-$\tau$, a method for utilizing key properties of the \emph{execution instance}, generating a tailored strategy that not only dampens the impact of stale updates, but also leverages fresh ones. We recover convergence bounds for adaptiveness functions satisfying the $\mathtt{ASAP.SGD}$ conditions for general, convex and non-convex problems, and establish novel bounds for ones satisfying the Polyak-Lojasiewicz property. We evaluate \textsc{tail}-$\tau$ with representative \emph{AsyncSGD} concurrent algorithms, for Deep Learning problems, showing \textsc{tail}-$\tau$ is a vital complement to \emph{AsyncSGD}, with (i)~persistent speedup in wall-clock convergence time in the parallelism spectrum, (ii)~considerably lower risk of non-convergence, as well as (iii)~precision levels for which original SGD implementations fail.

Present-day federated learning (FL) systems deployed over edge networks consists of a large number of workers with high degrees of heterogeneity in data and/or computing capabilities, which call for flexible worker participation in terms of timing, effort, data heterogeneity, etc. To satisfy the need for flexible worker participation, we consider a new FL paradigm called ``Anarchic Federated Learning'' (AFL) in this paper. In stark contrast to conventional FL models, each worker in AFL has the freedom to choose i) when to participate in FL, and ii) the number of local steps to perform in each round based on its current situation (e.g., battery level, communication channels, privacy concerns). However, such chaotic worker behaviors in AFL impose many new open questions in algorithm design. In particular, it remains unclear whether one could develop convergent AFL training algorithms, and if yes, under what conditions and how fast the achievable convergence speed is. Toward this end, we propose two Anarchic Federated Averaging (AFA) algorithms with two-sided learning rates for both cross-device and cross-silo settings, which are named AFA-CD and AFA-CS, respectively. Somewhat surprisingly, we show that, under mild anarchic assumptions, both AFL algorithms achieve the best known convergence rate as the state-of-the-art algorithms for conventional FL. Moreover, they retain the highly desirable {\em linear speedup effect} with respect of both the number of workers and local steps in the new AFL paradigm. We validate the proposed algorithms with extensive experiments on real-world datasets.

In federated learning (FL), model performance typically suffers from client drift induced by data heterogeneity, and mainstream works focus on correcting client drift. We propose a different approach named virtual homogeneity learning (VHL) to directly ``rectify'' the data heterogeneity. In particular, VHL conducts FL with a virtual homogeneous dataset crafted to satisfy two conditions: containing \emph{no} private information and being separable. The virtual dataset can be generated from pure noise shared across clients, aiming to calibrate the features from the heterogeneous clients. Theoretically, we prove that VHL can achieve provable generalization performance on the natural distribution. Empirically, we demonstrate that VHL endows FL with drastically improved convergence speed and generalization performance. VHL is the first attempt towards using a virtual dataset to address data heterogeneity, offering new and effective means to FL.

We present BRIEE, an algorithm for efficient reinforcement learning in Markov Decision Processes with block-structured dynamics (i.e., Block MDPs), where rich observations are generated from a set of unknown latent states. BRIEE interleaves latent states discovery, exploration, and exploitation together, and can provably learn a near-optimal policy with sample complexityscaling polynomially in the number of latent states, actions, and the time horizon, with no dependence on the size of the potentially infinite observation space.Empirically, we show that BRIEE is more sample efficient than the state-of-art Block MDP algorithm HOMER and other empirical RL baselines on challenging rich-observation combination lock problems which require deep exploration.

We give a sketching-based iterative algorithm that computes a $1+\varepsilon$ approximate solution for the ridge regression problem $\min_x \|Ax-b\|_2^2 +\lambda\|x\|_2^2$ where $A \in R^{n \times d}$ with $d \ge n$. Our algorithm, for a constant number of iterations (requiring a constant number of passes over the input), improves upon earlier work (Chowdhury et al.) by requiring that the sketching matrix only has a weaker Approximate Matrix Multiplication (AMM) guarantee that depends on $\varepsilon$, along with a constant subspace embedding guarantee. The earlier work instead requires that the sketching matrix has a subspace embedding guarantee that depends on $\varepsilon$. For example, to produce a $1+\varepsilon$ approximate solution in $1$ iteration, which requires $2$ passes over the input, our algorithm requires the OSNAP embedding to have $m= O(n\sigma^2/\lambda\varepsilon)$ rows with a sparsity parameter $s = O(\log(n))$, whereas the earlier algorithm of Chowdhury et al. with the same number of rows of OSNAP requires a sparsity $s = O(\sqrt{\sigma^2/\lambda\varepsilon} \cdot \log(n))$, where $\sigma = \opnorm{A}$ is the spectral norm of the matrix $A$. We also show that this algorithm can be used to give faster algorithms for kernel ridge regression. Finally, we show that the sketch size required for our algorithm is essentially optimal for a natural framework of algorithms for ridge regression by proving lower bounds on oblivious sketching matrices for AMM. The sketch size lower bounds for AMM may be of independent interest.

Multi-agent reinforcement learning (MARL) algorithms often suffer from an exponential sample complexity dependence on the number of agents, a phenomenon known as \emph{the curse of multiagents}. We address this challenge by investigating sample-efficient model-free algorithms in \emph{decentralized} MARL, and aim to improve existing algorithms along this line. For learning (coarse) correlated equilibria in general-sum Markov games, we propose \emph{stage-based} V-learning algorithms that significantly simplify the algorithmic design and analysis of recent works, and circumvent a rather complicated no-\emph{weighted}-regret bandit subroutine. For learning Nash equilibria in Markov potential games, we propose an independent policy gradient algorithm with a decentralized momentum-based variance reduction technique. All our algorithms are decentralized in that each agent can make decisions based on only its local information. Neither communication nor centralized coordination is required during learning, leading to a natural generalization to a large number of agents. Finally, we provide numerical simulations to corroborate our theoretical findings.

The von Neumann-Morgenstern (VNM) utility theorem shows that under certain axioms of rationality, decision-making is reduced to maximizing the expectation of some utility function. We extend these axioms to increasingly structured sequential decision making settings and identify the structure of the corresponding utility functions. In particular, we show that memoryless preferences lead to a utility in the form of a per transition reward and multiplicative factor on the future return. This result motivates a generalization of Markov Decision Processes (MDPs) with this structure on the agent's returns, which we call Affine-Reward MDPs. A stronger constraint on preferences is needed to recover the commonly used cumulative sum of scalar rewards in MDPs. A yet stronger constraint simplifies the utility function for goal-seeking agents in the form of a difference in some function of states that we call potential functions. Our necessary and sufficient conditions demystify the reward hypothesis that underlies the design of rational agents in reinforcement learning by adding an axiom to the VNM rationality axioms and motivates new directions for AI research involving sequential decision making.

We study online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$ resource constraints. By casting the learning process over a suitably defined space of strategy mixtures, we recover strong duality on a Lagrangian relaxation of the underlying optimization problem, even for general settings with non-convex reward and resource-consumption functions. Then, we provide the first best-of-both-worlds type framework for this setting, with no-regret guarantees both under stochastic and adversarial inputs. Our framework yields the same regret guarantees of prior work in the stochastic case. On the other hand, when budgets grow at least linearly in the time horizon, it allows us to provide a constant competitive ratio in the adversarial case, which improves over the $O(m \log T)$ competitive ratio of Immorlica et al. [FOCS'19]. Moreover, our framework allows the decision maker to handle non-convex reward and cost functions. We provide two game-theoretic applications of our framework to give further evidence of its flexibility.

Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or not. However, the answer from the oracle is correct only with probability $\frac{1}{2}+\frac{\delta}{2}$. The goal is to recover the hidden clusters with minimum number of noisy queries. Previous works have shown that the problem can be solved with $O(\frac{nk\log n}{\delta^2} + \text{poly}(k,\frac{1}{\delta}, \log n))$ queries, while $\Omega(\frac{nk}{\delta^2})$ queries is known to be necessary. So, for any values of $k$ and $\delta$, there is still a non-trivial gap between upper and lower bounds. In this work, we obtain the first matching upper and lower bounds for a wide range of parameters. In particular, a new polynomial time algorithm with $O(\frac{n(k+\log n)}{\delta^2} + \text{poly}(k,\frac{1}{\delta}, \log n))$ queries is proposed. Moreover, we prove a new lower bound of $\Omega(\frac{n\log n}{\delta^2})$, which, combined with the existing $\Omega(\frac{nk}{\delta^2})$ bound, matches our upper bound up to an additive $\text{poly}(k,\frac{1}{\delta},\log n)$ term. To obtain the new results, our main ingredient is an interesting connection between our problem and multi-armed bandit, which might provide useful insights for other similar problems.