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

Counterfactual Explanation and Causal Inference in Service of Robustness in Robot Control

We propose an architecture for training generative models of counterfactual conditionals of the form, 'can we modify event A to cause B instead of C?', motivated by applications in robot control. Using an 'adversarial training' paradigm, an image-based deep neural network model is trained to produce small and realistic modifications to an original image in order to cause user-defined effects. These modifications can be used in the design process of image-based robust control - to determine the ability of the controller to return to a working regime by modifications in the input space, rather than by adaptation. In contrast to conventional control design approaches, where robustness is quantified in terms of the ability to reject noise, we explore the space of counterfactuals that might cause a certain requirement to be violated, thus proposing an alternative model that might be more expressive in certain robotics applications. So, we propose the generation of counterfactuals as an approach to explanation of black-box models and the envisioning of potential movement paths in autonomous robotic control. Firstly, we demonstrate this approach in a set of classification tasks, using the well known MNIST and CelebFaces Attributes datasets. Then, addressing multi-dimensional regression, we demonstrate our approach in a reaching task with a physical robot, and in a navigation task with a robot in a digital twin simulation.Comment: 8 pages, 11 figures. To be published in the 10th IEEE International Conference on Development and Learning (ICDL), Valparaiso, Chil

Dynamic Regret Convergence Analysis and an Adaptive Regularization Algorithm for On-Policy Robot Imitation Learning

On-policy imitation learning algorithms such as DAgger evolve a robot control policy by executing it, measuring performance (loss), obtaining corrective feedback from a supervisor, and generating the next policy. As the loss between iterations can vary unpredictably, a fundamental question is under what conditions this process will eventually achieve a converged policy. If one assumes the underlying trajectory distribution is static (stationary), it is possible to prove convergence for DAgger. However, in more realistic models for robotics, the underlying trajectory distribution is dynamic because it is a function of the policy. Recent results show it is possible to prove convergence of DAgger when a regularity condition on the rate of change of the trajectory distributions is satisfied. In this article, we reframe this result using dynamic regret theory from the field of online optimization and show that dynamic regret can be applied to any on-policy algorithm to analyze its convergence and optimality. These results inspire a new algorithm, Adaptive On-Policy Regularization (AOR), that ensures the conditions for convergence. We present simulation results with cart-pole balancing and locomotion benchmarks that suggest AOR can significantly decrease dynamic regret and chattering as the robot learns. To our knowledge, this the first application of dynamic regret theory to imitation learning

Online Learning with Continuous Variations: Dynamic Regret and Reductions

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. In particular, we show monotone EPs admits a reduction to achieving sublinear static regret in COL. Using this new setup, we revisit the difficulty of sublinear dynamic regret. We prove a fundamental equivalence between achieving sublinear dynamic regret in COL and solving certain EPs. With this insight, we offer conditions for efficient algorithms that achieve sublinear dynamic regret, even when the losses are chosen adaptively without any a priori variation budget. Furthermore, we show for COL a reduction from dynamic regret to both static regret and convergence in the associated EP, allowing us to analyze the dynamic regret of many existing algorithms