Control Lyapunov functions are traditionally used to design a controller which ensures convergence to a desired state, yet deriving these functions for nonlinear systems remains a complex challenge. This paper presents a novel, sample-efficient method for neural approximation of nonlinear Lyapunov functions, leveraging self-supervised Reinforcement Learning (RL) to enhance training data generation, particularly for inaccurately represented regions of the state space. The proposed approach employs a data-driven World Model to train Lyapunov functions from off-policy trajectories. The method is validated on both standard and goal-conditioned robotic tasks, demonstrating faster convergence and higher approximation accuracy compared to the state-of-the-art neural Lyapunov approximation baseline. The code is available at: https://github.com/CAV-Research-Lab/SACLA.git

We provide the first known algorithm that provably achieves $\varepsilon$-optimality within $\widetilde{O}(1/\varepsilon)$ function evaluations for the discounted discrete-time linear quadratic regulator problem with unknown parameters, without relying on two-point gradient estimates. These estimates are known to be unrealistic in many settings, as they depend on using the exact same initialization, which is to be selected randomly, for two different policies. Our results substantially improve upon the existing literature outside the realm of two-point gradient estimates, which either leads to $\widetilde{O}(1/\varepsilon^2)$ rates or heavily relies on stability assumptions.

Designing machine learning algorithms that are accurate yet fair, not discriminating based on any sensitive attribute, is of paramount importance for society to accept AI for critical applications. In this article, we propose a novel fair representation learning method termed the Rényi Fair Information Bottleneck Method (RFIB) which incorporates constraints for utility, fairness, and compactness (compression) of representation, and apply it to image and tabular data classification. A key attribute of our approach is that we consider - in contrast to most prior work - both demographic parity and equalized odds as fairness constraints, allowing for a more nuanced satisfaction of both criteria. Leveraging a variational approach, we show that our objectives yield a loss function involving classical Information Bottleneck (IB) measures and establish an upper bound in terms of two Rényi measures of order$ \boldsymbol {\alpha }$on the mutual information IB term measuring compactness between the input and its encoded embedding. We study the influence of the$ \boldsymbol {\alpha }$parameter as well as two other tunable IB parameters on achieving utility/fairness trade-off goals, and show that the$ \boldsymbol {\alpha }$parameter gives an additional degree of freedom that can be used to control the compactness of the representation. Experimenting on three different image datasets (EyePACS, CelebA, and FairFace) and two tabular datasets (Adult and COMPAS), using both binary and categorical sensitive attributes, we show that on various utility, fairness, and compound utility/fairness metrics RFIB outperforms current state-of-the-art approaches.

We construct a system of interacting finite memory Pólya urns to model contagion spread in a network. The urns, which are composed of red and black balls (representing degrees of infection and healthiness, respectively) interact in the sense that the probability at any time instant of drawing a red ball for a given urn not only depends on that urn’s ratio of red balls, but also on the ratio of red balls in the other urns of the network, hence accounting for the effect of spatial contagion. The urns have a finite memory, M, in the sense that reinforcing (black or red) balls added to each urn at time t are only kept in that urn for M future time instants (until time t + M). The resulting vector of all urn drawing variables forms an Mth order time-invariant irreducible and aperiodic Markov chain. We analytically examine the properties of the underlying Markov process and derive its asymptotic behaviour for the case of homogeneous system parameters. We further use mean-field approximation to obtain a class of approximating linear and nonlinear dynamical systems for the non-homogeneous case. Finally, we present simulations to assess the quality of these mean-field approximations.

We investigate the use of parameterized families of information-theoretic measures to generalize the loss functions of generative adversarial networks (GANs) with the objective of improving performance. A new generator loss function, least kth-order GAN (LkGAN), is introduced, generalizing the least squares GANs (LSGANs) by using a kth-order absolute error distortion measure with k≥1 (which recovers the LSGAN loss function when k=2). It is shown that minimizing this generalized loss function under an (unconstrained) optimal discriminator is equivalent to minimizing the kth-order Pearson-Vajda divergence. Another novel GAN generator loss function is next proposed in terms of Rényi cross-entropy functionals with order α>0, α≠1. It is demonstrated that this Rényi-centric generalized loss function, which provably reduces to the original GAN loss function as α→1, preserves the equilibrium point satisfied by the original GAN based on the Jensen-Rényi divergence, a natural extension of the Jensen-Shannon divergence. Experimental results indicate that the proposed loss functions, applied to the MNIST and CelebA data sets, under both DCGAN and StyleGAN architectures, confer performance benefits by virtue of the extra degrees of freedom provided by the parameters k and α, respectively. More specifically, experiments show improvements with regard to the quality of the generated images as measured by the Fréchet inception distance score and training stability. While it was applied to GANs in this study, the proposed approach is generic and can be used in other applications of information theory to deep learning, for example, the issues of fairness or privacy in artificial intelligence.

We study the curing of epidemics of a network contagion, which is modelled using a variation of the classical Polya urn process that takes into account spatial infection among neighbouring nodes. We introduce several quantities for measuring the overall infection in the network and use them to formulate an optimal control problem for minimizing the average infection rate using limited curing resources. We prove the feasibility of this problem under high curing budgets by deriving conservative lower bounds on the amount of curing per node that turn our measures of network infection into supermartingales. We also provide a provably convergent gradient descent algorithm to find the allocation of curing under limited budgets. Motivated by the fact that this strategy is computationally expensive, we design a suit of heuristic methods that are locally implementable and nearly as effective. Extensive simulations run on large-scale networks demonstrate the effectiveness of our proposed strategies.

This paper considers games of incomplete information, where one player (the deceiver) has an informational advantage over the other (the mark) and intends to employ it for belief manipulation. We use the formalism of hypergames to represent the asymmetric information available to players. This framework allows us to formalize various notions of belief manipulation that revolve around the idea of the deceiver being able to make the mark believe that a particular action has lost its advantageous character. In the case when the deceiver does not mind revealing information to the mark as the game evolves, we provide a necessary condition and a sufficient condition for deceivability. In the case when the deceiver acts in a stealthy way, i.e., restricts its actions to those that do not contradict the belief of the mark, we fully characterize when deception is possible and design to find a sequence of deceiving actions. Our correctness guarantees for this strategy are based on a precise characterization of the acyclic structure of subjective hypergames. An example illustrates our results.

Nonlinear model for transverse dynamics of a vibrating beam is derived. In this modeling large deformation for beam is considered and consequently, high order curvature terms are not neglected. An adaptation method for applying large moments in the beam tip is developed using FEM. Port Hamiltonian interconnected system modeling is used to model the resulted configuration. The energy-based variable structure method is utilized to develop an interconnected controller with energy function associated with a set of Casimir functions relating to sliding surfaces. The energy function of the controller is chosen to make an attractive sliding surface for closed-loop system. Using this system, vibration of the nonlinear beam is stabilized in the desired shape of the beam.