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This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional…

We present a theoretical study of server-side optimization in federated learning. Our results are the first to show that the widely popular heuristic of scaling the client updates with an extra parameter is very useful in the context of…

Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…

Recently, a new multi-step temporal learning algorithm, called $Q(\sigma)$, unifies $n$-step Tree-Backup (when $\sigma=0$) and $n$-step Sarsa (when $\sigma=1$) by introducing a sampling parameter $\sigma$. However, similar to other…

Evolution Strategies (ES) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is widely used to solve difficult numerical optimization problems. We provide the first rigorous…

Adaptive gradient methods such as RMSProp and Adam use exponential moving estimate of the squared gradient to compute adaptive step sizes, achieving better convergence than SGD in face of noisy objectives. However, Adam can have undesirable…

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear…

Point cloud completion is essential for robust 3D perception in safety-critical applications such as robotics and augmented reality. However, existing models perform static inference and rely heavily on inductive biases learned during…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. Recent advances using the distributed gradient…

In this paper, we study numerical approximations for stochastic differential equations (SDEs) that use adaptive step sizes. In particular, we consider a general setting where decisions to reduce step sizes are allowed to depend on the…

We establish a continuous-time framework for analyzing Deep Q-Networks (DQNs) via stochastic control and Forward-Backward Stochastic Differential Equations (FBSDEs). Considering a continuous-time Markov Decision Process (MDP) driven by a…

In this paper, we introduce a unified framework for analyzing a large family of Q-learning algorithms, based on switching system perspectives and ODE-based stochastic approximation. We show that the nonlinear ODE models associated with…

In large-scale learning algorithms, the momentum term is usually included in the stochastic sub-gradient method to improve the learning speed because it can navigate ravines efficiently to reach a local minimum. However, step-size and…

Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…

Data similarity assumptions have traditionally been relied upon to understand the convergence behaviors of federated learning methods. Unfortunately, this approach often demands fine-tuning step sizes based on the level of data similarity.…

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…

In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…

Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However,…

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and…