Minimax optimization problems have attracted significant attention in recent years due to their widespread application in numerous machine learning models. To solve the minimax optimization problem, a wide variety of stochastic optimization methods have been proposed. However, most of them ignore the distributed setting where the training data is distributed on multiple workers. In this paper, we developed a novel decentralized stochastic gradient descent ascent method for the finite-sum minimax optimization problem. In particular, by employing the variance-reduced gradient, our method can achieve $O(\frac{\sqrt{n}\kappa^3}{(1-\lambda)^2\epsilon^2})$ sample complexity and $O(\frac{\kappa^3}{(1-\lambda)^2\epsilon^2})$ communication complexity for the nonconvex-strongly-concave minimax optimization problem. As far as we know, our work is the first one to achieve such theoretical complexities for this kind of problem. At last, we apply our method to optimize the AUC maximization problem and the experimental results confirm the effectiveness of our method.

We continue a long line of research aimed at proving convergence of depth 2 neural networks, trained via gradient descent, to a global minimum. Like in many previous works, our model has the following features: regression with quadratic loss function, fully connected feedforward architecture, RelU activations, Gaussian data instances and network initialization, adversarial labels. It is more general in the sense that we allow both layers to be trained simultaneously and at {\em different} rates. Our results improve on state-of-the-art [Oymak Soltanolkotabi 20] (training the first layer only) and [Nguyen 21, Section 3.2] (training both layers with Le Cun's initialization). We also report several simple experiments with synthetic data. They strongly suggest that, at least in our model, the convergence phenomenon extends well beyond the ``NTK regime''.

This study considers a federated learning setup where cost-sensitive and strategic agents train a learning model with a server. During each round, each agent samples a minibatch of training data and sends his gradient update. As an increasing function of his minibatch size choice, the agent incurs a cost associated with the data collection, gradient computation and communication. The agents have the freedom to choose their minibatch size and may even opt out from training. To reduce his cost, an agent may diminish his minibatch size, which may also cause an increase in the noise level of the gradient update. The server can offer rewards to compensate the agents for their costs and to incentivize their participation but she lacks the capability of validating the true minibatch sizes of the agents. To tackle this challenge, the proposed reward mechanism evaluates the quality of each agent's gradient according to the its distance to a reference which is constructed from the gradients provided by other agents. It is shown that the proposed reward mechanism has a cooperative Nash equilibrium in which the agents determine the minibatch size choices according to the requests of the server.

Federated learning has burgeoned recently in machine learning, giving rise to a variety of research topics. Popular optimization algorithms are based on the frameworks of the (stochastic) gradient descent methods or the alternating direction method of multipliers. In this paper, we deploy an exact penalty method to deal with federated learning and propose an algorithm, FedEPM, that enables to tackle four critical issues in federated learning: communication efficiency, computational complexity, stragglers' effect, and data privacy. Moreover, it is proven to be convergent and testified to have high numerical performance.

Combinatorial optimization (CO) layers in machine learning (ML) pipelines are a powerful tool to tackle data-driven decision tasks, but they come with two main challenges. First, the solution of a CO problem often behaves as a piecewise constant function of its objective parameters. Given that ML pipelines are typically trained using stochastic gradient descent, the absence of slope information is very detrimental. Second, standard ML losses do not work well in combinatorial settings. A growing body of research addresses these challenges through diverse methods. Unfortunately, the lack of well-maintained implementations slows down the adoption of CO layers. In this paper, building upon previous works, we introduce a probabilistic perspective on CO layers, which lends itself naturally to approximate differentiation and the construction of structured losses. We recover many approaches from the literature as special cases, and we also derive new ones. Based on this unifying perspective, we present InferOpt.jl, an open-source Julia package that 1) allows turning any CO oracle with a linear objective into a differentiable layer, and 2) defines adequate losses to train pipelines containing such layers. Our library works with arbitrary optimization algorithms, and it is fully compatible with Julia's ML ecosystem. We demonstrate its abilities using a pathfinding problem on video game maps as guiding example, as well as three other applications from operations research.

In constrained reinforcement learning (C-RL), an agent seeks to learn from the environment a policy that maximizes the expected cumulative reward while satisfying minimum requirements in secondary cumulative reward constraints. Several algorithms rooted in sampled-based primal-dual methods have been recently proposed to solve this problem in policy space. However, such methods are based on stochastic gradient descent ascent algorithms whose trajectories are connected to the optimal policy only after a mixing output stage that depends on the algorithm's history. As a result, there is a mismatch between the behavioral policy and the optimal one. In this work, we propose a novel algorithm for constrained RL that does not suffer from these limitations. Leveraging recent results on regularized saddle-flow dynamics, we develop a novel stochastic gradient descent-ascent algorithm whose trajectories converge to the optimal policy almost surely.

Here we demonstrate that desynchronous implementation of coupled learning is effective in self-adjusting resistor networks, in both simulation and experiment. Furthermore, we Learning is a special case of memory [1, 2], where the goal show that desynchronous learning can actually improve performance is to encode targeted functional responses in a network [3-by allowing the system to evolve indefinitely, escaping 6]. Artificial Neural Networks (ANNs) are complex functions local minima. We draw a direct analogy between stochastic designed to achieve such targeted responses. These networks gradient descent and desynchronous learning, and show are trained by using gradient descent on a cost function, they have similar effects on the learning degrees of freedom which evolves the system's parameters until a local minimum in our system. Thus we are able to remove the final vestige of is found [7, 8]. Typically, this algorithm is modified non-locality from our physics-driven learning network, moving such that subsections (batches) of data are used at each training it closer to biological implementations of learning. The step, effectively adding noise to the gradient calculation, ability to learn with entirely independent learning elements is known as Stochastic Gradient Descent (SGD) [9]. This algorithm expected to greatly improve the scalability of such physical produces more generalizable results [10-12], i.e. better learning systems.

Kartik Chandra, Audrey Xie, Jonathan Ragan-Kelley and Erik Meijer won a NeurIPS 2022 outstanding paper award for their work Gradient descent: the ultimate optimizer. Here, they tell us more about their work, the methodology and their main findings. Our paper studies the classic problem of "hyperparameter optimization". Nearly all of today's machine learning algorithms use a process called "stochastic gradient descent" (SGD) to train neural networks. SGD requires users to pick certain settings, or "hyperparameters," before running it.

We consider the constrained sampling problem where the goal is to sample from a distribution $\pi(x)\propto e^{-f(x)}$ and $x$ is constrained on a convex body $\mathcal{C}\subset \mathbb{R}^d$. Motivated by penalty methods from optimization, we propose penalized Langevin Dynamics (PLD) and penalized Hamiltonian Monte Carlo (PHMC) that convert the constrained sampling problem into an unconstrained one by introducing a penalty function for constraint violations. When $f$ is smooth and the gradient is available, we show $\tilde{\mathcal{O}}(d/\varepsilon^{10})$ iteration complexity for PLD to sample the target up to an $\varepsilon$-error where the error is measured in terms of the total variation distance and $\tilde{\mathcal{O}}(\cdot)$ hides some logarithmic factors. For PHMC, we improve this result to $\tilde{\mathcal{O}}(\sqrt{d}/\varepsilon^{7})$ when the Hessian of $f$ is Lipschitz and the boundary of $\mathcal{C}$ is sufficiently smooth. To our knowledge, these are the first convergence rate results for Hamiltonian Monte Carlo methods in the constrained sampling setting that can handle non-convex $f$ and can provide guarantees with the best dimension dependency among existing methods with deterministic gradients. We then consider the setting where unbiased stochastic gradients are available. We propose PSGLD and PSGHMC that can handle stochastic gradients without Metropolis-Hasting correction steps. When $f$ is strongly convex and smooth, we obtain an iteration complexity of $\tilde{\mathcal{O}}(d/\varepsilon^{18})$ and $\tilde{\mathcal{O}}(d\sqrt{d}/\varepsilon^{39})$ respectively in the 2-Wasserstein distance. For the more general case, when $f$ is smooth and non-convex, we also provide finite-time performance bounds and iteration complexity results. Finally, we test our algorithms on Bayesian LASSO regression and Bayesian constrained deep learning problems.

This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear neural network. Moreover, even if the weights remain random, we get their precise law along the training dynamics, and prove a quantitative convergence result of the linear predictor in terms of the number of neurons. We finally study the continuous-time limit obtained for infinitely wide linear neural networks and show that the linear predictors of the neural network converge at an exponential rate to the minimal $\ell_2$-norm minimizer of the risk.