We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph. For such graphs, the proposed algorithm has a sample complexity of n = Ω(J −2 min log p), where p is the number of variables, and Jmin is the minimum (absolute) edge potential in the model. We also establish nonasymptotic necessary and sufficient conditions for structure estimation.

We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for nonconvex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allows for efficient optimization. Using this property we show that stochastic gradient descent converges to a local minimum in a polynomial number of iterations. To the best of our knowledge this is the first work that gives global convergence guarantees for stochastic gradient descent on nonconvex functions with exponentially many local minima and saddle points.Our analysis can be applied to orthogonal tensor decomposition, which is widely used in learning a rich class of latent variable models. We propose a new optimization formulation for the tensor decomposition problem that has strict saddle property. As a result we get the first online algorithm for orthogonal tensor decomposition with global convergence guarantee.

Evaluating the worst-case performance of a reinforcement learning (RL) agent under the strongest/optimal adversarial perturbations on state observations (within some constraints) is crucial for understanding the robustness of RL agents. However, finding the optimal adversary is challenging, in terms of both whether we can find the optimal attack and how efficiently we can find it. Existing works on adversarial RL either use heuristics-based methods that may not find the strongest adversary, or directly train an RL-based adversary by treating the agent as a part of the environment, which can find the optimal adversary but may become intractable in a large state space. In this paper, we propose a novel attacking algorithm which has an RL-based "director" searching for the optimal policy perturbation, and an "actor" crafting state perturbations following the directions from the director (i.e. the actor executes targeted attacks). Our proposed algorithm, PA-AD, is theoretically optimal against an RL agent and significantly improves the efficiency compared with prior RL-based works in environments with large or pixel state spaces. Empirical results show that our proposed PA-AD universally outperforms state-of-the-art attacking methods in a wide range of environments. Our method can be easily applied to any RL algorithms to evaluate and improve their robustness.Preprint. Under review.

In cognitive radio networks, multiple spectrum opportunities can be used together to satisfy the service requirement by spectrum aggregation. In this paper, an admission control algorithm and a spectrum assignment strategy are proposed in order for both increasing the spectrum aggregation aware access capacity and decreasing the channel switch times when the channel states change. Considering different bandwidth requirement of secondary users, the proposed greedy admission algorithm takes limited aggregation capability into account. The channel switch times of secondary users at sensing moments is minimized based on the prediction of primary activities and the corresponding channel state transitions. The concept of outage probability is introduced into the scheme to indicate the probability of channel switch. The numerical results show the performance improvement of the proposed algorithms.

Poisoning attacks, although have been studied extensively in supervised learning, are not well understood in Reinforcement Learning (RL), especially in deep RL. Prior works on poisoning RL usually either assume the attacker knows the underlying Markov Decision Process (MDP), or directly apply the poisoning methods in supervised learning to RL. In this work, we build a generic poisoning framework for online RL via a comprehensive investigation of heterogeneous types/victims of poisoning attacks in RL, considering the unique challenges in RL such as data no longer being i.i.d. Without any prior knowledge of the MDP, we propose a strategic poisoning algorithm called Vulnerability-Aware Adversarial Critic Poison (VA2C-P), which works for most policy-based deep RL agents, using a novel metric, stability radius in RL, that measures the vulnerability of RL algorithms. Experiments on multiple deep RL agents and multiple environments show that our poisoning algorithm successfully prevents agents from learning a good policy, with a limited attacking budget. Our experiment results demonstrate varying vulnerabilities of different deep RL agents in multiple environments, benefiting the understanding and applications of deep RL under security threat scenarios.Preprint. Under review.