Related papers: On minimizing cyclists' ascent times
This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying…
The phenomenon of model-wise double descent, where the test error peaks and then reduces as the model size increases, is an interesting topic that has attracted the attention of researchers due to the striking observed gap between theory…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
One of the challenges for climbing gyms is to find out popular routes for the climbers to improve their services and optimally use their infrastructure. This problem must be addressed preserving both the privacy and convenience of the…
We develop a convergence-rate analysis of momentum with cyclical step-sizes. We show that under some assumption on the spectral gap of Hessians in machine learning, cyclical step-sizes are provably faster than constant step-sizes. More…
Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent…
Trajectory optimization for autonomous vehicles usually relies on the kinematic bicycle model because of its computational simplicity. However, when the planned trajectory is executed under the true vehicle dynamics, which include lateral…
We use reinforcement learning to find strategies that allow microswimmers in turbulence to avoid regions of large strain. This question is motivated by the hypothesis that swimming microorganisms tend to avoid such regions to minimise the…
In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant…
AdaBoost is one of the most popular ML algorithms. It is simple to implement and often found very effective by practitioners, while still being mathematically elegant and theoretically sound. AdaBoost's interesting behavior in practice…
In this paper, the impact of escaping in couples on the evacuation dynamics has been investigated via experiments and modeling. Two sets of experiments have been implemented, in which pedestrians are asked to escape either in individual or…
Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle. However, activity fluctuations also appear over a wide range of temporal scales, from days to a few…
The second-order sub-optimal sliding mode control (SMC), known in the literature for the last two decades, is extended by a control-off mode which allows for saving energy during the finite time convergence. The systems with relative degree…
There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…
For a connected graph $G$, the average hitting time $\alpha(G)$ and the Kemeny's constant $\kappa(G)$ are two similar quantities, both measuring the time for the random walk on $G$ to travel between two randomly chosen vertices. We prove…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
Stability of bipedal systems in frontal plane is affected by the hip offset, to the extent that adjusting stride time using feedforward retraction and extension of the legs can lead to stable oscillations without feedback control. This…
The relation among instantaneous, mean and average velocities in one-dimensional motion with constant acceleration is studied. It was shown that the instant velocity evaluated in the time $t_{p}=\left(t_2+t_1\right)/2$ is similar to the…
Intrinsically motivated artificial agents learn advantageous behavior without externally-provided rewards. Previously, it was shown that maximizing mutual information between agent actuators and future states, known as the empowerment…
In the absence of acceleration, the velocity formula gives "distance travelled equals speed multiplied by time". For a broad class of Markov chains such as circulant Markov chains or random walk on complete graphs, we prove a probabilistic…