Related papers: On minimizing cyclists' ascent times

We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…

This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a…

The minimum energy, and, more generally, the minimum cost, to transmit one bit of information has been recently derived for bursty communication when information is available infrequently at random times at the transmitter. This result…

We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…

Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…

For a transition between two stable states, the committor is the probability that the dynamics leads to one stable state before the other. It can be estimated from trajectory data by minimizing an expression for the transition rate that…

In this article we present an approach that enables joint wind speed and wind power forecasts for a wind park. We combine a multivariate seasonal time varying threshold autoregressive moving average (TVARMA) model with a power threshold…

Allowing for adversarial contamination and heavy tails, we study testing whether the mean of a high-dimensional random vector equals zero. Because standard max-tests based on sample averages are highly non-robust, we propose a max-test…

In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…

This paper introduces an improved social force model for companion group that incorporates relative weight attraction. Based on the traditional social force model, the interaction forces among individuals within leader-follower groups are…

Continuous-time reinforcement learning tasks commonly use discrete steps of fixed cycle times for actions. As practitioners need to choose the action-cycle time for a given task, a significant concern is whether the hyper-parameters of the…

We prove some theorems about self-avoiding walks attached to an impenetrable surface (i.e. positive walks) and subject to a force. Specifically we show the force dependence of the free energy is identical when the force is applied at the…

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…

In neural network training, RMSProp and Adam remain widely favoured optimisation algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. Additionally,…

Let $\xi(n, x)$ be the local time at $x$ for a recurrent one-dimensional random walk in random environment after $n$ steps, and consider the maximum $\xi^*(n) = \max_x \xi(n,x)$. It is known that $\limsup \xi^*(n)/n$ is a positive constant…

This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…

Due to the redundancy of our motor system, movements can be performed in many ways. While multiple motor control strategies can all lead to the desired behavior, they result in different joint and muscle forces. This creates opportunities…