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Generating Adversarial Disturbances for Controller Verification

arXiv.org Machine Learning

We consider the problem of generating maximally adversarial disturbances for a given controller assuming only blackbox access to it. We propose an online learning approach to this problem that adaptively generates disturbances based on control inputs chosen by the controller. The goal of the disturbance generator is to minimize regret versus a benchmark disturbance-generating policy class, i.e., to maximize the cost incurred by the controller as well as possible compared to the best possible disturbance generator in hindsight (chosen from a benchmark policy class). In the setting where the dynamics are linear and the costs are quadratic, we formulate our problem as an online trust region (OTR) problem with memory and present a new online learning algorithm (MOTR) for this problem. We prove that this method competes with the best disturbance generator in hindsight (chosen from a rich class of benchmark policies that includes linear-dynamical disturbance generating policies). We demonstrate our approach on two simulated examples: (i) synthetically generated linear systems, and (ii) generating wind disturbances for the popular PX4 controller in the AirSim simulator.


Online Control with Adversarial Disturbances

arXiv.org Machine Learning

We study the control of a linear dynamical system with adversarial disturbances (as opposed to statistical noise). The objective we consider is one of regret: we desire an online control procedure that can do nearly as well as that of a procedure that has full knowledge of the disturbances in hindsight. Our main result is an efficient algorithm that provides nearly tight regret bounds for this problem. From a technical standpoint, this work generalizes upon previous work in two main aspects: our model allows for adversarial noise in the dynamics, and allows for general convex costs.


Adaptive Regret for Control of Time-Varying Dynamics

arXiv.org Machine Learning

We consider regret minimization for online control with time-varying linear dynamical systems. The metric of performance we study is adaptive policy regret, or regret compared to the best policy on {\it any interval in time}. We give an efficient algorithm that attains first-order adaptive regret guarantees for the setting of online convex optimization with memory. We also show that these first-order bounds are nearly tight. This algorithm is then used to derive a controller with adaptive regret guarantees that provably competes with the best linear dynamical controller on any interval in time. We validate these theoretical findings experimentally on (1) simulations of time-varying linear dynamics and disturbances, and (2) the non-linear inverted pendulum benchmark.


A Regret Minimization Approach to Multi-Agent Control

arXiv.org Machine Learning

We study the problem of multi-agent control of a dynamical system with known dynamics and adversarial disturbances. Our study focuses on optimal control without centralized precomputed policies, but rather with adaptive control policies for the different agents that are only equipped with a stabilizing controller. We give a reduction from any (standard) regret minimizing control method to a distributed algorithm. The reduction guarantees that the resulting distributed algorithm has low regret relative to the optimal precomputed joint policy. Our methodology involves generalizing online convex optimization to a multi-agent setting and applying recent tools from nonstochastic control derived for a single agent. We empirically evaluate our method on a model of an overactuated aircraft. We show that the distributed method is robust to failure and to adversarial perturbations in the dynamics.


Non-Stochastic Control with Bandit Feedback

arXiv.org Machine Learning

The crucial component in RL/control that allows learning is the feedback, or reward/penalty, which the agent iteratively observes and reacts to. While some signal is necessary for learning, different applications have different feedback to the learning agent. In many reinforcement learning and control problems it is unrealistic to assume that the learner has feedback for actions other than their own. One example is in game-playing, such as the game of Chess, where a player can observe the adversary's move for their own choice of play, but it is unrealistic to expect knowledge of the adversary's play for any possible move. This type of feedback is commonly known in the learning literature as "bandit feedback". Learning in Markov Decision Processes (MDP) is a general and difficult problem for which there are no known algorithms that have sublinear dependence on the number of states. For this reason we look at structured MDPs, and in particular the model of control in Linear Dynamical Systems (LDS), a highly structured special case that is known to admit more efficient methods as compared to general RL. In this paper we study learning in linear dynamical systems with bandit feedback.