skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, September 13 until 2:00 AM ET on Saturday, September 14 due to maintenance. We apologize for the inconvenience.


This content will become publicly available on November 1, 2024

Title: Reward Learning With Intractable Normalizing Functions
Robots can learn to imitate humans by inferring what the human is optimizing for. One common framework for this is Bayesian reward learning, where the robot treats the human's demonstrations and corrections as observations of their underlying reward function. Unfortunately, this inference is doubly-intractable: the robot must reason over all the trajectories the person could have provided and all the rewards the person could have in mind. Prior work uses existing robotic tools to approximate this normalizer. In this letter, we group previous approaches into three fundamental classes and analyze the theoretical pros and cons of their approach. We then leverage recent research from the statistics community to introduce Double MH reward learning, a Monte Carlo method for asymptotically learning the human's reward in continuous spaces. We extend Double MH to conditionally independent settings (where each human correction is viewed as completely separate) and conditionally dependent environments (where the human's current correction may build on previous inputs). Across simulations and user studies, our proposed approach infers the human's reward parameters more accurately than the alternate approximations when learning from either demonstrations or corrections.  more » « less
Award ID(s):
2222468
NSF-PAR ID:
10494587
Author(s) / Creator(s):
;
Publisher / Repository:
IEEE
Date Published:
Journal Name:
IEEE Robotics and Automation Letters
Volume:
8
Issue:
11
ISSN:
2377-3774
Page Range / eLocation ID:
7511 to 7518
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Reward learning as a method for inferring human intent and preferences has been studied extensively. Prior approaches make an implicit assumption that the human maintains a correct belief about the robot's domain dynamics. However, this may not always hold since the human's belief may be biased, which can ultimately lead to a misguided estimation of the human's intent and preferences, which is often derived from human feedback on the robot's behaviors. In this paper, we remove this restrictive assumption by considering that the human may have an inaccurate understanding of the robot. We propose a method called Generalized Reward Learning with biased beliefs about domain dynamics (GeReL) to infer both the reward function and human's belief about the robot in a Bayesian setting based on human ratings. Due to the complex forms of the posteriors, we formulate it as a variational inference problem to infer the posteriors of the parameters that govern the reward function and human's belief about the robot simultaneously. We evaluate our method in a simulated domain and with a user study where the user has a bias based on the robot's appearances. The results show that our method can recover the true human preferences while subject to such biased beliefs, in contrast to prior approaches that could have misinterpreted them completely. 
    more » « less
  2. Designing reward functions is a difficult task in AI and robotics. The complex task of directly specifying all the desirable behaviors a robot needs to optimize often proves challenging for humans. A popular solution is to learn reward functions using expert demonstrations. This approach, however, is fraught with many challenges. Some methods require heavily structured models, for example, reward functions that are linear in some predefined set of features, while others adopt less structured reward functions that may necessitate tremendous amounts of data. Moreover, it is difficult for humans to provide demonstrations on robots with high degrees of freedom, or even quantifying reward values for given trajectories. To address these challenges, we present a preference-based learning approach, where human feedback is in the form of comparisons between trajectories. We do not assume highly constrained structures on the reward function. Instead, we employ a Gaussian process to model the reward function and propose a mathematical formulation to actively fit the model using only human preferences. Our approach enables us to tackle both inflexibility and data-inefficiency problems within a preference-based learning framework. We further analyze our algorithm in comparison to several baselines on reward optimization, where the goal is to find the optimal robot trajectory in a data-efficient way instead of learning the reward function for every possible trajectory. Our results in three different simulation experiments and a user study show our approach can efficiently learn expressive reward functions for robotic tasks, and outperform the baselines in both reward learning and reward optimization.

     
    more » « less
  3. This paper presents a framework to learn the reward function underlying high-level sequential tasks from demonstrations. The purpose of reward learning, in the context of learning from demonstration (LfD), is to generate policies that mimic the demonstrator’s policies, thereby enabling imitation learning. We focus on a human-robot interaction(HRI) domain where the goal is to learn and model structured interactions between a human and a robot. Such interactions can be modeled as a partially observable Markov decision process (POMDP) where the partial observability is caused by uncertainties associated with the ways humans respond to different stimuli. The key challenge in finding a good policy in such a POMDP is determining the reward function that was observed by the demonstrator. Existing inverse reinforcement learning(IRL) methods for POMDPs are computationally very expensive and the problem is not well understood. In comparison, IRL algorithms for Markov decision process (MDP) are well defined and computationally efficient. We propose an approach of reward function learning for high-level sequential tasks from human demonstrations where the core idea is to reduce the underlying POMDP to an MDP and apply any efficient MDP-IRL algorithm. Our extensive experiments suggest that the reward function learned this way generates POMDP policies that mimic the policies of the demonstrator well. 
    more » « less
  4. This paper proposes a novel approach that enables a robot to learn an objective function incrementally from human directional corrections. Existing methods learn from human magnitude corrections; since a human needs to carefully choose the magnitude of each correction, those methods can easily lead to over-corrections and learning inefficiency. The proposed method only requires human directional corrections — corrections that only indicate the direction of an input change without indicating its magnitude. We only assume that each correction, regardless of its magnitude, points in a direction that improves the robot’s current motion relative to an unknown objective function. The allowable corrections satisfying this assumption account for half of the input space, as opposed to the magnitude corrections which have to lie in a shrinking level set. For each directional correction, the proposed method updates the estimate of the objective function based on a cutting plane method, which has a geometric interpretation. We have established theoretical results to show the convergence of the learning process. The proposed method has been tested in numerical examples, a user study on two human-robot games, and a real-world quadrotor experiment. The results confirm the convergence of the proposed method and further show that the method is significantly more effective (higher success rate), efficient/effortless (less human corrections needed), and potentially more accessible (fewer early wasted trials) than the state-of-the-art robot learning frameworks. 
    more » « less
  5. Reward functions are a common way to specify the objective of a robot. As designing reward functions can be extremely challenging, a more promising approach is to directly learn reward functions from human teachers. Importantly, data from human teachers can be collected either passively or actively in a variety of forms: passive data sources include demonstrations (e.g., kinesthetic guidance), whereas preferences (e.g., comparative rankings) are actively elicited. Prior research has independently applied reward learning to these different data sources. However, there exist many domains where multiple sources are complementary and expressive. Motivated by this general problem, we present a framework to integrate multiple sources of information, which are either passively or actively collected from human users. In particular, we present an algorithm that first utilizes user demonstrations to initialize a belief about the reward function, and then actively probes the user with preference queries to zero-in on their true reward. This algorithm not only enables us combine multiple data sources, but it also informs the robot when it should leverage each type of information. Further, our approach accounts for the human’s ability to provide data: yielding user-friendly preference queries which are also theoretically optimal. Our extensive simulated experiments and user studies on a Fetch mobile manipulator demonstrate the superiority and the usability of our integrated framework. 
    more » « less