Hongyi Ren

Masoud Badiei Khuzani, Varun Vasudevan, Hongyi Ren et al.

We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle from a given mixture policy class characterized by the convex hull of a set of known base policies. To learn the coefficients of the mixture model, we recast the problem as an approximate linear programming (ALP) formulation for MDPs, where the feature vectors correspond to the occupation measures of the base policies defined on the state-action space. We then propose a projection-free stochastic primal-dual method with the Bregman divergence to solve the characterized ALP. Furthermore, we analyze the probably approximately correct (PAC) sample complexity of the proposed stochastic algorithm, namely the number of queries required to achieve near optimal objective value. We also propose a modification of our proposed algorithm with the polytope constraint sampling for the smoothed ALP, where the restriction to lower bounding approximations are relaxed. In addition, we apply the proposed algorithms to a queuing problem, and compare their performance with a penalty function algorithm. The numerical results illustrates that the primal-dual achieves better efficiency and low variance across different trials compared to the penalty function method.

Masoud Badiei Khuzani, Hongyi Ren, Md Tauhidul Islam et al.

We propose a novel data-driven method to learn a mixture of multiple kernels with random features that is certifiabaly robust against adverserial inputs. Specifically, we consider a distributionally robust optimization of the kernel-target alignment with respect to the distribution of training samples over a distributional ball defined by the Kullback-Leibler (KL) divergence. The distributionally robust optimization problem can be recast as a min-max optimization whose objective function includes a log-sum term. We develop a mini-batch biased stochastic primal-dual proximal method to solve the min-max optimization. To debias the minibatch algorithm, we use the Gumbel perturbation technique to estimate the log-sum term. We establish theoretical guarantees for the performance of the proposed multiple kernel learning method. In particular, we prove the consistency, asymptotic normality, stochastic equicontinuity, and the minimax rate of the empirical estimators. In addition, based on the notion of Rademacher and Gaussian complexities, we establish distributionally robust generalization bounds that are tighter than previous known bounds. More specifically, we leverage matrix concentration inequalities to establish distributionally robust generalization bounds. We validate our kernel learning approach for classification with the kernel SVMs on synthetic dataset generated by sampling multvariate Gaussian distributions with differernt variance structures. We also apply our kernel learning approach to the MNIST data-set and evaluate its robustness to perturbation of input images under different adversarial models. More specifically, we examine the robustness of the proposed kernel model selection technique against FGSM, PGM, C\&W, and DDN adversarial perturbations, and compare its performance with alternative state-of-the-art multiple kernel learning paradigms.