Ke Sun

Ke Sun, Iñaki Esnaola, Antonia M. Tulino et al.

The learning data requirements are analyzed for the construction of stealth attacks in state estimation. In particular, the training data set is used to compute a sample covariance matrix that results in a random matrix with a Wishart distribution. The ergodic attack performance is defined as the average attack performance obtained by taking the expectation with respect to the distribution of the training data set. The impact of the training data size on the ergodic attack performance is characterized by proposing an upper bound for the performance. Simulations on the IEEE 30-Bus test system show that the proposed bound is tight in practical settings.

Ke Sun, Samir M. Perlaza, Alain Jean-Marie

In this paper, $2\times2$ zero-sum games are studied under the following assumptions: $(1)$ One of the players (the leader) commits to choose its actions by sampling a given probability measure (strategy); $(2)$ The leader announces its action, which is observed by its opponent (the follower) through a binary channel; and $(3)$ the follower chooses its strategy based on the knowledge of the leader's strategy and the noisy observation of the leader's action. Under these conditions, the equilibrium is shown to always exist. Interestingly, even subject to noise, observing the actions of the leader is shown to be either beneficial or immaterial for the follower. More specifically, the payoff at the equilibrium of this game is upper bounded by the payoff at the Stackelberg equilibrium (SE) in pure strategies; and lower bounded by the payoff at the Nash equilibrium, which is equivalent to the SE in mixed strategies.Finally, necessary and sufficient conditions for observing the payoff at equilibrium to be equal to its lower bound are presented. Sufficient conditions for the payoff at equilibrium to be equal to its upper bound are also presented.

Ke Sun, Yingnan Zhao, Wulong Liu et al.

The empirical success of distributional reinforcement learning (RL) highly relies on the choice of distribution divergence equipped with an appropriate distribution representation. In this paper, we propose \textit{Sinkhorn distributional RL (SinkhornDRL)}, which leverages Sinkhorn divergence, a regularized Wasserstein loss, to minimize the difference between current and target Bellman return distributions. Theoretically, we prove the contraction properties of SinkhornDRL, aligning with the interpolation nature of Sinkhorn divergence between Wasserstein distance and Maximum Mean Discrepancy (MMD). The introduced SinkhornDRL enriches the family of distributional RL algorithms, contributing to interpreting the algorithm behaviors compared with existing approaches by our investigation into their relationships. Empirically, we show that SinkhornDRL consistently outperforms or matches existing algorithms on the Atari games suite and particularly stands out in the multi-dimensional reward setting. \thanks{Code is available in \url{https://github.com/datake/SinkhornDistRL}.}.

Ke Sun, Inaki Esnaola, Samir M. Perlaza et al.

Gaussian random attacks that jointly minimize the amount of information obtained by the operator from the grid and the probability of attack detection are presented. The construction of the attack is posed as an optimization problem with a utility function that captures two effects: firstly, minimizing the mutual information between the measurements and the state variables; secondly, minimizing the probability of attack detection via the Kullback-Leibler divergence between the distribution of the measurements with an attack and the distribution of the measurements without an attack. Additionally, a lower bound on the utility function achieved by the attacks constructed with imperfect knowledge of the second order statistics of the state variables is obtained. The performance of the attack construction using the sample covariance matrix of the state variables is numerically evaluated. The above results are tested in the IEEE 30-Bus test system.

Frank Nielsen, Ke Sun

Clustering categorical distributions in the finite-dimensional probability simplex is a fundamental task met in many applications dealing with normalized histograms. Traditionally, the differential-geometric structures of the probability simplex have been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the dualistic information-geometric structure induced by a smooth dissimilarity measure, the Kullback-Leibler divergence. In this work, we introduce for clustering tasks a novel computationally-friendly framework for modeling geometrically the probability simplex: The {\em Hilbert simplex geometry}. In the Hilbert simplex geometry, the distance is the non-separable Hilbert's metric distance which satisfies the property of information monotonicity with distance level set functions described by polytope boundaries. We show that both the Aitchison and Hilbert simplex distances are norm distances on normalized logarithmic representations with respect to the $\ell_2$ and variation norms, respectively. We discuss the pros and cons of those different statistical modelings, and benchmark experimentally these different kind of geometries for center-based $k$-means and $k$-center clustering. Furthermore, since a canonical Hilbert distance can be defined on any bounded convex subset of the Euclidean space, we also consider Hilbert's geometry of the elliptope of correlation matrices and study its clustering performances compared to Fröbenius and log-det divergences.