Continuous Online Learning and New Insights to Online Imitation Learning

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function changes continuously across rounds with respect to the learner's decisions. We show that COL covers and more appropriately describes many interesting applications, from general equilibrium problems (EPs) to optimization in episodic MDPs. Using this new setup, we revisit the difficulty of achieving sublinear dynamic regret. We prove that there is a fundamental equivalence between achieving sublinear dynamic regret in COL and solving certain EPs, and we present a reduction from dynamic regret to both static regret and convergence rate of the associated EP. At the end, we specialize these new insights into online imitation learning and show improved understanding of its learning stability

Learning from Imperfect Demonstrations from Agents with Varying Dynamics

Imitation learning enables robots to learn from demonstrations. Previous imitation learning algorithms usually assume access to optimal expert demonstrations. However, in many real-world applications, this assumption is limiting. Most collected demonstrations are not optimal or are produced by an agent with slightly different dynamics. We therefore address the problem of imitation learning when the demonstrations can be sub-optimal or be drawn from agents with varying dynamics. We develop a metric composed of a feasibility score and an optimality score to measure how useful a demonstration is for imitation learning. The proposed score enables learning from more informative demonstrations, and disregarding the less relevant demonstrations. Our experiments on four environments in simulation and on a real robot show improved learned policies with higher expected return.Comment: Accpeted by ICRA 202

Explaining Fast Improvement in Online Imitation Learning

Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this phenomenon. Let $\xi$ denote the policy class bias and assume the online IL loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of online IL with stochastic feedback, the policy improves in $\tilde{O}(1/N + \sqrt{\xi/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in online IL has two benefits: both the policy improvement speed increases and the performance bias decreases.Comment: 22 pages, 2 figure