When Will Generative Adversarial Imitation Learning Algorithms Attain Global Convergence

Generative adversarial imitation learning (GAIL) is a popular inverse reinforcement learning approach for jointly optimizing policy and reward from expert trajectories. A primary question about GAIL is whether applying a certain policy gradient algorithm to GAIL attains a global minimizer (i.e., yields the expert policy), for which existing understanding is very limited. Such global convergence has been shown only for the linear (or linear-type) MDP and linear (or linearizable) reward. In this paper, we study GAIL under general MDP and for nonlinear reward function classes (as long as the objective function is strongly concave with respect to the reward parameter). We characterize the global convergence with a sublinear rate for a broad range of commonly used policy gradient algorithms, all of which are implemented in an alternating manner with stochastic gradient ascent for reward update, including projected policy gradient (PPG)-GAIL, Frank-Wolfe policy gradient (FWPG)-GAIL, trust region policy optimization (TRPO)-GAIL and natural policy gradient (NPG)-GAIL. This is the first systematic theoretical study of GAIL for global convergence.

Robust Stochastic Bandit Algorithms under Probabilistic Unbounded Adversarial Attack

The multi-armed bandit formalism has been extensively studied under various attack models, in which an adversary can modify the reward revealed to the player. Previous studies focused on scenarios where the attack value either is bounded at each round or has a vanishing probability of occurrence. These models do not capture powerful adversaries that can catastrophically perturb the revealed reward. This paper investigates the attack model where an adversary attacks with a certain probability at each round, and its attack value can be arbitrary and unbounded if it attacks. Furthermore, the attack value does not necessarily follow a statistical distribution. We propose a novel sample median-based and exploration-aided UCB algorithm (called med-E-UCB) and a median-based $epsilon$-greedy algorithm (called med-$epsilon$-greedy). Both of these algorithms are provably robust to the aforementioned attack model. More specifically we show that both algorithms achieve $mathcal{O}(log T)$ pseudo-regret (i.e., the optimal regret without attacks). We also provide a high probability guarantee of $mathcal{O}(log T)$ regret with respect to random rewards and random occurrence of attacks. These bounds are achieved under arbitrary and unbounded reward perturbation as long as the attack probability does not exceed a certain constant threshold. We provide multiple synthetic simulations of the proposed algorithms to verify these claims and showcase the inability of existing techniques to achieve sublinear regret. We also provide experimental results of the algorithm operating in a cognitive radio setting using multiple software-defined radios.