Fundamental Performance Limits for Sensor-Based Robot Control and Policy Learning

Our goal is to develop theory and algorithms for establishing fundamental limits on performance for a given task imposed by a robot's sensors. In order to achieve this, we define a quantity that captures the amount of task-relevant information provided by a sensor. Using a novel version of the generalized Fano inequality from information theory, we demonstrate that this quantity provides an upper bound on the highest achievable expected reward for one-step decision making tasks. We then extend this bound to multi-step problems via a dynamic programming approach. We present algorithms for numerically computing the resulting bounds, and demonstrate our approach on three examples: (i) the lava problem from the literature on partially observable Markov decision processes, (ii) an example with continuous state and observation spaces corresponding to a robot catching a freely-falling object, and (iii) obstacle avoidance using a depth sensor with non-Gaussian noise. We demonstrate the ability of our approach to establish strong limits on achievable performance for these problems by comparing our upper bounds with achievable lower bounds (computed by synthesizing or learning concrete control policies).

Robust Control Under Uncertainty via Bounded Rationality and Differential Privacy

The rapid development of affordable and compact high-fidelity sensors (e.g., cameras and LIDAR) allows robots to construct detailed estimates of their states and environments. However, the availability of such rich sensor information introduces two technical challenges: (i) the lack of analytic sensing models, which makes it difficult to design controllers that are robust to sensor failures, and (ii) the computational expense of processing the high-dimensional sensor information in real time. This paper addresses these challenges using the theory of differential privacy, which allows us to (i) design controllers with bounded sensitivity to errors in state estimates, and (ii) bound the amount of state information used for control (i.e., to impose bounded rationality). The resulting framework approximates the separation principle and allows us to derive an upper-bound on the cost incurred with a faulty state estimator in terms of three quantities: the cost incurred using a perfect state estimator, the magnitude of state estimation errors, and the level of differential privacy. We demonstrate the efficacy of our framework numerically on different robotics problems, including nonlinear system stabilization and motion planning.

Invariant Policy Optimization: Towards Stronger Generalization in Reinforcement Learning

A fundamental challenge in reinforcement learning is to learn policies that generalize beyond the operating domain experienced during training. In this paper, we approach this challenge through the following invariance principle: an agent must find a representation such that there exists an action-predictor built on top of this representation that is simultaneously optimal across all training domains. Intuitively, the resulting invariant policy enhances generalization by finding causes of successful actions. We propose a novel learning algorithm, Invariant Policy Optimization (IPO), that explicitly enforces this principle and learns an invariant policy during training. We compare our approach with standard policy gradient methods and demonstrate significant improvements in generalization performance on unseen domains for Linear Quadratic Regulator (LQR) problems and our own benchmark in the MiniGrid Gym environment.

Learning Task-Driven Control Policies via Information Bottlenecks

This paper presents a reinforcement learning approach to synthesizing task-driven control policies for robotic systems equipped with rich sensory modalities (e.g., vision or depth). Standard reinforcement learning algorithms typically produce policies that tightly couple control actions to the entirety of the system's state and rich sensor observations. As a consequence, the resulting policies can often be sensitive to changes in task-irrelevant portions of the state or observations (e.g., changing background colors). In contrast, the approach we present here learns to create a task-driven representation that is used to compute control actions. Formally, this is achieved by deriving a policy gradient-style algorithm that creates an information bottleneck between the states and the task-driven representation; this constrains actions to only depend on task-relevant information. We demonstrate our approach in a thorough set of simulation results on multiple examples including a grasping task that utilizes depth images and a ball-catching task that utilizes RGB images. Comparisons with a standard policy gradient approach demonstrate that the task-driven policies produced by our algorithm are often significantly more robust to sensor noise and task-irrelevant changes in the environment.

Task-Driven Estimation and Control via Information Bottlenecks

Our goal is to develop a principled and general algorithmic framework for task-driven estimation and control for robotic systems. State-of-the-art approaches for controlling robotic systems typically rely heavily on accurately estimating the full state of the robot (e.g., a running robot might estimate joint angles and velocities, torso state, and position relative to a goal). However, full state representations are often excessively rich for the specific task at hand and can lead to significant computational inefficiency and brittleness to errors in state estimation. In contrast, we present an approach that eschews such rich representations and seeks to create task-driven representations. The key technical insight is to leverage the theory of information bottlenecks}to formalize the notion of a "task-driven representation" in terms of information theoretic quantities that measure the minimality of a representation. We propose novel iterative algorithms for automatically synthesizing (offline) a task-driven representation (given in terms of a set of task-relevant variables (TRVs)) and a performant control policy that is a function of the TRVs. We present online algorithms for estimating the TRVs in order to apply the control policy. We demonstrate that our approach results in significant robustness to unmodeled measurement uncertainty both theoretically and via thorough simulation experiments including a spring-loaded inverted pendulum running to a goal location.