Continuous Online Learning and New Insights to Online Imitation Learning

Abstract

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

“…, a N , s N }, we aim to learn a policy π * that best matches the demonstration trajectories. Note that we focus on the offline imitation setting as employed in [3], [7], where a set of demonstrations are provided ahead of time instead of gradually incrementing our dataset as in online imitation learning [33].…”

Explaining Fast Improvement in Online Imitation Learning

“…The interactions of these properties make the classic adversary-style online learning analysis taken by Ross et al [2] overly conservative, creating a mismatch between provable theoretical guarantees and the learning phenomena observed in practice. This reality gap has motivated researchers to study deeper the theoretical underpinnings of OPO [12][13][14].…”