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In this paper, we address the distributed prescribed-time convex optimization (DPTCO) for a class of networked Euler-Lagrange systems under undirected connected graphs. By utilizing position-dependent measured gradient value of local…

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…

The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…

This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying…

Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

This paper presents a high-order differentiator for delayed measurement signal. The proposed differentiator not only can correct the delay in signal, but aslo can estimate the undelayed derivatives. The differentiator consists of two-step…

Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is…

This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on…

We study distributed differentiation, where agents in a networked system estimate the average of local time-varying signals and their derivatives under mild assumptions on the agents' signals and their first and second derivatives. Existing…

Differential temporal difference (TD) methods are value-based reinforcement learning algorithms that have been proposed for infinite-horizon problems. They rely on reward centering, where each reward is centered by the average reward. This…

Many models such as Long Short Term Memory (LSTMs), Gated Recurrent Units (GRUs) and transformers have been developed to classify time series data with the assumption that events in a sequence are ordered. On the other hand, fewer models…

Validation is a major challenge in differentiable programming. The state of the art is based on algorithmic differentiation. Consistency of first-order tangent and adjoint programs is defined by a well-known first-order differential…

Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these…

We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacobi equations and prove a general convergence result for this class of schemes. A typical filtered scheme is obtained mixing a high-order scheme and a…

The success of deep learning over the past decade mainly relies on gradient-based optimisation and backpropagation. This paper focuses on analysing the performance of first-order gradient-based optimisation algorithms, gradient descent and…

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…

Decentralized optimization over time-varying graphs has been increasingly common in modern machine learning with massive data stored on millions of mobile devices, such as in federated learning. This paper revisits the widely used…

Time series generation is a crucial research topic in the area of decision-making systems, which can be particularly important in domains like autonomous driving, healthcare, and, notably, robotics. Recent approaches focus on learning in…

In reinforcement learning, temporal difference-based algorithms can be sample-inefficient: for instance, with sparse rewards, no learning occurs until a reward is observed. This can be remedied by learning richer objects, such as a model of…