Dušan M. Stipanović

Theodoros Mamalis, Dusan Stipanovic, Petros Voulgaris

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies almost-sure convergence rates of the Stochastic Gradient Descent method when instead of deterministic, its learning rate becomes stochastic. In particular, its learning rate is equipped with a multiplicative stochasticity, producing a stochastic learning rate scheme. Theoretical results show accelerated almost-sure convergence rates of Stochastic Gradient Descent in a nonconvex setting when using an appropriate stochastic learning rate, compared to a deterministic-learning-rate scheme. The theoretical results are verified empirically.

Theodoros Mamalis, Dusan Stipanovic, Petros Voulgaris

In this work, multiplicative stochasticity is applied to the learning rate of stochastic optimization algorithms, giving rise to stochastic learning-rate schemes. In-expectation theoretical convergence results of Stochastic Gradient Descent equipped with this novel stochastic learning rate scheme under the stochastic setting, as well as convergence results under the online optimization settings are provided. Empirical results consider the case of an adaptively uniformly distributed multiplicative stochasticity and include not only Stochastic Gradient Descent, but also other popular algorithms equipped with a stochastic learning rate. They demonstrate noticeable optimization performance gains, with respect to their deterministic-learning-rate versions.

Thiago Marinho, Massi Amrouche, Dusan Stipanovic et al.

Biological evidence shows that animals are capable of evading eminent collision without using depth information, relying solely on looming stimuli. In robotics, collision avoidance among uncooperative vehicles requires measurement of relative distance to the obstacle. Small, low-cost mobile robots and UAVs might be unable to carry distance measuring sensors, like LIDARS and depth cameras. We propose a control framework suitable for a unicycle-like vehicle moving in a 2D plane that achieves collision avoidance. The control strategy is inspired by the reaction of invertebrates to approaching obstacles, relying exclusively on line-of-sight (LOS) angle, LOS angle rate, and time-to-collision as feedback. Those quantities can readily be estimated from a monocular camera vision system onboard a mobile robot. The proposed avoidance law commands the heading angle to circumvent a moving obstacle with unknown position, while the velocity controller is left as a degree of freedom to accomplish other mission objectives. Theoretical guarantees are provided to show that minimum separation between the vehicle and the obstacle is attained regardless of the exogenous tracking controller.

Shankar A. Deka, Dušan M. Stipanović, Claire J. Tomlin

Convolutional and recurrent neural networks have been widely employed to achieve state-of-the-art performance on classification tasks. However, it has also been noted that these networks can be manipulated adversarially with relative ease, by carefully crafted additive perturbations to the input. Though several experimentally established prior works exist on crafting and defending against attacks, it is also desirable to have theoretical guarantees on the existence of adversarial examples and robustness margins of the network to such examples. We provide both in this paper. We focus specifically on recurrent architectures and draw inspiration from dynamical systems theory to naturally cast this as a control problem, allowing us to dynamically compute adversarial perturbations at each timestep of the input sequence, thus resembling a feedback controller. Illustrative examples are provided to supplement the theoretical discussions.

Vicenc Rubies-Royo, Roberto Calandra, Dusan M. Stipanovic et al.

To use neural networks in safety-critical settings it is paramount to provide assurances on their runtime operation. Recent work on ReLU networks has sought to verify whether inputs belonging to a bounded box can ever yield some undesirable output. Input-splitting procedures, a particular type of verification mechanism, do so by recursively partitioning the input set into smaller sets. The efficiency of these methods is largely determined by the number of splits the box must undergo before the property can be verified. In this work, we propose a new technique based on shadow prices that fully exploits the information of the problem yielding a more efficient generation of splits than the state-of-the-art. Results on the Airborne Collision Avoidance System (ACAS) benchmark verification tasks show a considerable reduction in the partitions generated which substantially reduces computation times. These results open the door to improved verification methods for a wide variety of machine learning applications including vision and control.