Related papers: Adaptive control mechanisms in gradient descent al…
The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…
A continuous adaptive control design is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. The key feature of this design is a robust integral of the sign of the…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…
This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of…
This paper presents a discrete-time passivity-based analysis of the gradient descent method for a class of functions with sector-bounded gradients. Using a loop transformation, it is shown that the gradient descent method can be interpreted…
One of the main features of adaptive systems is an oscillatory convergence that exacerbates with the speed of adaptation. Recently it has been shown that Closed-loop Reference Models (CRMs) can result in improved transient performance over…
A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from its minimizers. In this work, we argue that this belief is inaccurate. We show…
Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many…
This paper bridges optimization and control, and presents a novel closed-loop control framework based on natural gradient descent, offering a trajectory-oriented alternative to traditional cost-function tuning. By leveraging the Fisher…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly…
We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a…
Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization rather than on global, worst-case constants. Key to our proofs is directional smoothness, a…
Stochastic gradient descent (SGD) is a powerful optimization technique that is particularly useful in online learning scenarios. Its convergence analysis is relatively well understood under the assumption that the data samples are…
This work presents a solution to the adaptive tracking control of Euler Lagrange systems with guaranteed tracking and parameter estimation error convergence. Specifically a concurrent learning based update rule fused by the filtered version…
Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output…
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…