Graph Inverse Reinforcement Learning from Diverse Videos Kumar Jonathan Hansen*
Jangir
[Figure]
Abstract: Research on Inverse Reinforcement Learning (IRL) from third-person videos has shown encouraging results on removing the need for manual reward design for robotic tasks.
However, most prior works are still limited by training from a relatively restricted domain of videos.
In this paper, we argue that the true potential of third-person IRL lies in increasing the diversity of videos for better scaling.
To learn a reward function from diverse videos, we propose to perform graph abstraction on the videos followed by temporal matching in the graph space to measure the task progress.
Our insight is that a task can be described by entity interactions that form a graph, and this graph abstraction can help remove irrelevant information such as textures, resulting in more robust reward functions.
We evaluate our approach, GraphIRL , on cross-embodiment learning in X-MAGICAL and learning from human demonstrations for real-robot manipulation.
We show signiﬁcant improvements in robustness to diverse video demonstrations over previous approaches, and even achieve better results than manual reward design on a real robot pushing task.
Videos are available at https://sateeshkumar21.github.io/GraphIRL/ .
Introduction
Deep Reinforcement Learning (RL) is a powerful general-purpose framework for learning behavior policies from high-dimensional interaction data, and has led to a multitude of impressive feats in application areas such as game-playing [1] and robotics [2, 3].
Through interaction with an unknown environment, RL agents iteratively improve their policy by learning to maximize a reward signal, which has the potential to be used in lieu of hand-crafted control policies.
However, the performance of policies learned by RL is found to be highly dependent on the careful speciﬁcation of reward functions and, as a result, crafting a good reward function may require signiﬁcant domain knowledge and technical expertise.
As an alternative to manual design of reward functions, inverse RL (IRL) has emerged as a promising paradigm for policy learning.
By framing the reward speciﬁcation as a learning problem, operators can specify a reward function based on video examples.
While imitation learning typically requires demonstrations from a ﬁrst-person perspective, IRL can in principle learn a reward function, i.e. , a measure of task progression, from any perspective, including third-person videos of humans performing a task.
This has positive implications for data collection, since it is often far easier for humans to capture demonstrations in third-person.
Although IRL from third-person videos is appealing because of its perceived ﬂexibility, learning a good reward function from raw video data comes with a variety of challenges.
This is perhaps unsurprising, considering the visual and functional diversity that such data contains.
For example, the task of pushing an object across a table may require different motions depending on the embodiment of the agent.
A recent method for cross-embodiment IRL, dubbed XIRL [4], learns to capture task progression from videos in a self-supervised manner by enforcing temporal cycle-consistency constraints.
While XIRL can in principle consume any video demonstration, we observe that its ability to learn task progression degrades substantially when the visual appearance of the video demonstrations do not match that of the target environment for RL.
Therefore, it is natural to ask the question: can we learn to imitate others from (a limited number of) diverse third-person videos?
In this work, we demonstrate that it is indeed possible.
Our key insight is that, while videos may be of great visual diversity, their underlying scene structure and agent-object interactions can be abstracted via a graph representation.
Speciﬁcally, instead of directly using images, we extract object bounding boxes from each frame using an off-the-shelf detector, and construct a graph abstraction where each object is represented as a node in the graph.
Often – in robotics tasks – the spatial location of an object by itself may not convey the full picture of the task at hand.
For instance, to understand a task like Peg in Box (shown in Figure 1), we need to also take into account how the agent interacts with the object.
Therefore, we propose to employ Interaction Networks [5] on our graph representation to explicitly model interactions between entities.
To train our model, we follow [4, 6] and apply a temporal cycle consistency loss, which (in our framework) yields task-speciﬁc yet embodiment- and domain-agnostic feature representations.
We validate our method empirically on a set of simulated cross-domain cross-embodiment tasks from
X-MAGICAL [4], as well as three vision-based robotic manipulation tasks.
To do so, we collect a diverse set of demonstrations that vary in visual appearance, embodiment, object categories, and scene conﬁguration; X-MAGICAL demonstrations are collected in simulation, whereas our manipulation demonstrations consist of real-world videos of humans performing tasks.
We ﬁnd our method to outperform a set of strong baselines when learning from visually diverse demonstrations, while simultaneously matching their performance in absence of diversity.
Further, we demonstrate that vision-based policies trained with our learned reward perform tasks with greater precision than humandesigned reward functions, and successfully transfer to a real robot setup with only approximate correspondence to the simulation environment.
Thus, our proposed framework completes the cycle of learning rewards from real-world human demonstrations, learning a policy in simulation using learned rewards, and ﬁnally deployment of the learned policy on physical hardware.
Related Work
Learning from demonstration.
Conventional imitation learning methods require access to expert demonstrations comprised of observations and corresponding ground-truth actions for every time step [7, 8, 9, 10], for which kinesthetic teaching or teleoperation are the primary modes of data collection in robotics.
To scale up learning, video demonstrations are recorded with human operating the same gripper that the robot used, which also allows direct behaviro cloning [11, 12].
More recently, researchers have developed methods that instead infer actions from data via a learned forward [13] or inverse [14, 15] dynamics model.
However, this approach still makes the implicit assumption that imitator and demonstrator share a common observation and action space, and are therefore not directly applicable to the cross-domain cross-embodiment problem setting that we consider.
Inverse RL.
To address the aforementioned limitations, inverse RL has been proposed [16, 17, 18, 19, 20, 21] and it has recently emerged as a promising paradigm for cross-embodiment imitation in particular [22, 23, 24, 25, 26, 27, 28, 4, 29].
For example, Schmeckpeper et al.
[22] proposes a method for integrating video demonstrations without corresponding actions into off-policy RL algorithms via a latent inverse dynamics model and heuristic reward assignment, and Zakka et al. [4] (XIRL) learns a reward function from video demonstrations using temporal cycle-consistency and trains an RL agent to maximize the learned rewards.
In practice, however, inverse RL methods such as XIRL are found to require limited visual diversity in demonstrations.
Our work extends
XIRL to the setting of diverse videos by introducing a graph abstraction that models agent-object and object-object interactions while still enforcing temporal cycle-consistency.
Object-centric representations.
have been proposed in many forms at the intersection of computer vision and robotics.
For example, object-centric scene graphs can be constructed for integrated task and motion planning [30, 31, 32], navigation [33, 34], relational inference [35, 36], dynamics modeling [5, 37, 38, 39, 40, 41], model predictive control [42, 43, 44], grasping [45, 46] or visual imitation learning [47, 48, 49].
Similar to our work, Sieb et al.
[49] propose to abstract video demonstrations as object-centric graphs for the problem of single-video cross-embodiment imitation, and act by minimizing the difference between the demonstration graph and a graph constructed from observations captured at each step.
As such, their method is limited to same-domain visual trajectory following, whereas we learn a general alignment function for cross-domain cross-embodiment imitation and leverage Interaction Networks [5] for modeling graph-abstracted spatial interactions rather than relying on heuristics.
Our Approach
In this section, we describe our main contribution, which is a self-supervised method for learning a visually invariant reward function directly from a set of diverse third-person video demonstrations via a graph abstraction.
Our Graph Inverse Reinforcement Learning (GraphIRL) framework, shown in Figure 2, consists of building an object-centric graph abstraction of the video demonstrations and then learn an embedding space that captures task progression by exploiting the temporal cue in the videos.
This embedding space is then used to construct a domain invariant and embodiment invariant reward function which can be used to train any standard reinforcement learning algorithm.
Problem Formulation.
Given a task T , our approach takes a dataset of video demonstrations
D =
{ V 1 , V 2 , . .
, V n } .
Each video consists of image frames { I i 1 , I i 2 , . .
, I ik } where i denotes the video frame index and k denotes the total number of frames in V i .
Given D , our goal is to learn a reward function that can be used to solve the task T for any robotic environment.
Notably, we do not assume access to any action information of the expert demonstrations, and our approach does not require objects or embodiments in the target environment to share appearance with demonstrations.
3.1 Representation Learning
To learn task-speciﬁc representations in a self-supervised manner, we take inspiration from Dwibedi et al.
[6] and employ a temporal cycle consistency loss.
However, instead of directly using images, we propose a novel object-centric graph representation, which allows us to learn an embedding space that not only captures task-speciﬁc features, but depends solely on the spatial conﬁguration of objects and their interactions.
We here detail each component of our approach to representation learning.
Object-Centric Representation.
Given video frames { I i 1 , I i 2 , . . .
, I ik } , we ﬁrst extract object bounding boxes from each frame using an off-the-shelf detector.
Given N bounding boxes for an image, we represent each bounding box as a 4 + m dimensional vector o j = { x 1 , y 1 , x 2 , y 2 , d 1 , d 2 , . . .
, d m } , where the ﬁrst 4 dimensions represent the leftmost and rightmost corners of the bounding box, and the remaining m dimensions encode distances between the centroids of the objects.
For each frame
I ij we extract an object-centric representation I (cid:48) ij = { o 1 , o 2 , . . .
, o m } such that we can represent our dataset of demonstrations as D (cid:48) =
{ V (cid:48) 1 , V (cid:48) 2 , . .
, V (cid:48) n } where V (cid:48) i is the sequence of bounding boxes corresponding to video V i .
Subsequent sections describe how we learn representations given D (cid:48) .
Spatial Interaction Encoder.
Taking inspiration from recent approaches on modeling physical object dynamics [5, 37], we propose a Spatial Interaction Encoder Network to explicitly model object-object interactions.
Speciﬁcally, given a sequence V (cid:48) i from D (cid:48) , we model each element I (cid:48) as a graph, G =
( O, R ) , where O is the set of objects { o 1 , o 2 , . . .
, o m } , m is the total number of objects in I (cid:48) , and R denotes the relationship between objects ( i.e. , whether two objects interact with each other).
For simplicity, all objects are connected with all other objects in the graph such that
R = { ( i, j ) | i (cid:54) =
j ∧ i ≤ m ∧ j ≤ m } .
We use a fully-connected graph because this makes the least assumption about the problem and task speciﬁc object interaction structure could then be learned directly from the data.
We compose an object embedding for each of o i ∈
O by combining self and interactional representations as follows:
[Equation]
where f s ( o i ) represents the self or independent representation of an object, f in represents the interactional representation, i.e. , how it interacts with other objects in the scene, f o is the ﬁnal object embedding, and ( , ) represents concatenation. Here, the encoders φ s , φ in and φ agg denote Multi layer
Perceptron (MLP) networks respectively.
We emphasize that the expression for f in ( · ) implies that the object embedding f o ( . ) depends on all other objects in the scene; this term allows us to model relationships of an object with the others.
The ﬁnal output from the spatial interaction encoder ψ ( · ) for object representation I (cid:48) is the mean of all object encodings:
[Equation]
The spatial interaction encoder is then optimized using the temporal alignment loss introduced next.
Temporal Alignment Loss .
Taking inspiration from prior works on video representatoin learning [6, 50, 51], we use temporal alignment as a proxy for video representation learning.
Given a pair of videos, the task of self-supervised alignment implicitly assumes that there exists true semantic correspondence between the two sequences, i.e. , both videos share a common semantic space.
These works have shown that optimizing for alignment leads to representations that could be used for tasks that require understanding task progression such as action-classiﬁcation.
This is because in order to solve for alignment, a learning model has to learn features that are (1) common across most videos and (2) exhibit temporal ordering.
For a sufﬁciently large dataset with single task, the most common visual features would be distinct phases of a task that appear in all videos and if the task has small permutations, these distinct features would also exhibit temporal order.
In such scenarios, the representations learned by optimizing for alignment are task-speciﬁc and invariant to changes in viewpoints, motions and embodiments.
In this work, we employ Temporal Cycle Consistency (TCC) [6] loss to learn temporal alignment.
TCC optimizes for alignment by learning an embedding space that maximizes one-to-one nearest neighbour mappings between sequences.
This is achieved through a loss that maximizes for cycleconsistent nearest neighbours given a pair of video sequences.
In our case, the cycle consistency is applied on the graph abstraction instead of image features as done in the aforementioned video alignment methods.
Speciﬁcally, given D (cid:48) , we sample a pair of bounding box sequences V (cid:48)
i =
{ I (cid:48) i 1 , . .
, I (cid:48)
im i } and V (cid:48)
j = { I (cid:48) j 1 , . .
, I (cid:48) jm j } , we extract embeddings by applying our spatial interaction encoder deﬁned in Equation 2.
Thus, we obtain the encoded features S i = { ψ ( I (cid:48) i 1 ) , . . .
, ψ ( I (cid:48)
im i ) } and
S j
=
ψ ( I (cid:48) j 1 ) , . . . , ψ ( I (cid:48) jm j ) } .
For the n th element in S i , we ﬁrst compute its nearest neighbour, υ nij , in S j and then compute the probability that it cycles-back to n , β kijn as
[Equation]
The cycle consistency loss for n th element can be computed as L ijn = ( µ nij − n ) 2 , where µ nij = (cid:80) mik β kijn k is the expected value of frame index n as we cycle back.
The overall TCC loss is then deﬁned by summing over all pairs of sequence embeddings ( S i , S j ) in the data, i.e. , L nij = (cid:80) ijn L nij .
3.2 Reinforcement Learning
We learn a task-speciﬁc embedding space by optimizing for temporal alignment.
In this section, we deﬁne how to go from this embedding space to a reward function that measures task progression.
For constructing the reward function, we leverage the insight from Zakka et al.
[4] that in a task-speciﬁc embedding space, we can use euclidean distance as a notion of task progression, i.e. , frames far apart in the embedding space will be far apart in terms of task progression and vice versa.
We therefore choose to deﬁne our reward function as r ( o ) = − 1 c
|| ψ ( o ) − g || 2 , with g = (cid:80) ni
=1 ψ ( I (cid:48)
im i ) , where o is the current observation, ψ is our Interaction Networks-based encoder from Section 3, g is the representative goal frame, m i is the length of sequence V (cid:48)
i and c is a scaling factor.
This deﬁnition gives us a dense reward because as the observed state gets closer and closer to the goal, the reward starts going down and approaches zero when the goal and current observation are close in embedding space; refer to supplementary material for qualitative analysis of the learned reward function.
After constructing the learned reward, we can use it to train any standard RL algorithm.
We note that, unlike previous approaches [22, 4], our method does not use any environment reward to improve performance, and instead relies solely on the learned reward, which our experiments demonstrate is sufﬁcient for solving diverse robotic manipulation tasks.
Experiments
In this section, we demonstrate how our approach uses diverse video demonstrations to learn a reward function that generalizes to unseen domains.
In particular, we are interested in answering the questions: (1) How do vision-based methods for IRL perform when learning from demonstrations that exhibit domain shift ? (2) Can our approach learn a stronger reward signal under this challenging setting?
To that end, we ﬁrst conduct experiments on the X-MAGICAL benchmark [4].
We then conduct experiments on multiple robot manipulation tasks using a diverse set of demonstrations.
Implementation Details.
All MLPs have 2 hidden layers, and the embedding layer outputs features of size 128 in all experiments.
We use Soft Actor-Critic (SAC) [52] as backbone RL algorithm for all methods.
For experiments on X-MAGICAL, we follow Zakka et al.
[4] and learn a state-based policy.
For robotic manipulation experiments, we learn a multi-view image-based SAC policy [53].
For fair comparison, we only change the learned reward function across methods and keep the RL setup identical.
Refer to the supplementary material for further implementation details.
Baselines.
We compare against multiple vision-based approaches that learn rewards in a selfsupervised manner: (1) XIRL [4] that learns a reward function by applying the TCC [6] loss on demonstration video sequences, (2) TCN [54] which is a self-supervised contrastive method for video representation learning that optimizes for temporally disentangled representations, and (3) LIFS [55] that learns an invariant feature space using a dynamic time warping-based contrastive loss.
Lastly, we also compare against the manually designed (4) Environment Reward from Jangir et al.
The environment reward baseline is an oracle method since it is a dense reward and is carefully designed for the task under consideration.
For learning-based baselines, we use a ResNet-18 encoder pretrained on ImageNet [56] classiﬁcation.
See supplementary material for details. [Figure] L-stick Gripper
S-stick M [Figure] stick
L-stick [Figure] 4.1 Experimental Setup We conduct experiments under two settings: the Sweep-to-Goal task from X-MAGICAL [4], and robotic manipulation tasks with an xArm robot both in simulation and on a real robot setup.
We describe our experimental setup under these two settings in the following.
X-MAGICAL.
We choose to extend X-MAGICAL [4], a 2D simulation environment for crossembodiment imitation learning.
On this benchmark, we consider a multi-object sweeping task, where the agent must push three objects towards a static goal region.
We utilize two variants of the X-MAGICAL benchmark, which we denote as Standard (original) and Diverse (ours) environments, shown in Figure 3.
Standard only randomizes the position of objects, whereas Diverse also randomizes visual appearance.
We consider a set of four unique embodiments { gripper, shortstick, medium-stick, long-stick } .
In particular, we conduct experiments in the cross-environment and cross-embodiment setting where we learn a reward function in the Standard environment onheld-out embodiments and do RL in the Diverse environment on 1 target embodiment, or vice-versa.
This provides an additional layer of difﬁculty for the RL agent as visual randomizations show the brittleness of vision-based IRL methods. [Figure] [Figure]
Robotic Manipulation.
Figure 1 shows initial and success conﬁgurations for each of the three task that we consider: (1) Reach in which the agent needs to reach a goal (red disc) with its end-effector, (2) Push in which the goal is to push a cube to a goal position, and (3) Peg in Box where the goal is to put a peg tied to the robot’s end-effector inside a box.
The last task is particularly difﬁcult because it requires geometric 3D understanding of the objects.
We collect a total of 256 andvideo demonstrations for Reach and Peg in Box , respectively, and use 198 videos provided from
Schmeckpeper et al.
[22] for Push .
The videos consist of human actors performing the same tasks but with a number of diverse objects and goal markers, as well as varied positions of objects.
Unlike the data collected by Schmeckpeper et al.
[22], we do not ﬁx the goal position in our demonstrations.
Additionally, we do not require the demonstrations to resemble the robotic environment in terms of appearance or distribution of goal location.
In order to detect objects in our training demonstrations, we use a trained model from Shan et al. Refer to supplementary for details on robot platform.
4.2 Results
X-MAGICAL.
Results for the cross-embodiment and cross-environment setting are shown in Figure 4.
When trained on Standard , our method performs signiﬁcantly better than vision-based baselines ( e.g. , 0 .
58 GraphIRL for gripper vs 0 .
35 for XIRL and 0 .
99 GraphIRL for longstick vs 0 .
56 XIRL).
We conjecture that vision-based baselines struggle with visual variations in the environment, which our method is unaffected by due to its graph abstraction.
Additionally, we note that XIRL performs strongly when trained on Diverse .
This could be because the Diverse environment contains some examples that are visually the same as Standard environment.
To verify this, we conduct an experiment where we remove the shape (Square) and color (Red) used in Standard environment from the random conﬁgurations for Diverse environment and then construct a new set of demonstration.
We refer to this environment as Diverse (Out Of Distribution) .
In this setting, XIRL’s performance drops signiﬁcantly for 3 out of 4 embodiments.
Robotic manipulation in simulation.
In this section, we answer the core question of our work: can we learn to imitate others from diverse third-person videos?
In particular, we collect human demonstrations for manipulation tasks as explained in Section 4.1 and learn a reward function as explained in Section 3.
This is a challenging setting because as shown in Figure 1, the collected data and robotic environments belong to different domains and do not share any appearance characteristics.
Further, unlike previous works [22, 4], we do not use any environment reward as an additional supervision to the reinforcement learning agent.
Figure 5 presents our results.
For the Reach task,
GraphIRL and environment reward achieve a success rate of 1 . 0 , while other baseline methods are substantially behind GraphIRL (e.g. 0 .
477 XIRL and 0 .
155 TCN).
In the Push setting, vision-based baseline methods still perform poorly.
Similar to Reach , XIRL performed the best out of the visionbased baselines with a success rate of 0 . 187 , and GraphIRL performed better than environment [Figure] reward with a success rate of 0 . 832 .
The Peg in Box task is rigorous to solve since it requires 3-d reasoning and a precise reward function.
Here, while all vision-based methods fail, GraphIRL solves the task with 55 .
2% success rate.
Overall, our GraphIRL method is able to solve 2D and 3D reasoning tasks with a real-robot without a hand-designed reward function or access to 3D scene information.
Real robot experiments.
Finally, we deploy the learned policies on a real robot.
For each experiment, we conduct 15 trials per method and report the average success rate.
Results are shown in Table 1.
Interestingly, we ﬁnd that GraphIRL outperforms XIRL in all three tasks on the real robot setup, and on Push , GraphIRL performs better than the environment reward speciﬁcally designed for the task (e.g. 0 .
93 Environment Reward vs 0 .
86 GraphIRL) which is in line with our ﬁndings in simulation.
4.3 Ablations
Variant
[Figure] Impact of Modelling Spatial Interactions.
We study the impact of modeling object-object spatial interactions using Spatial Interaction Encoder Network (IN) described in Section 3.1.
Speciﬁcally, we replace our proposed encoder component with an Multi-Layer Perceptron (MLP) by concatenating representations of all objects into a single vector and then feeding it to a 3-layer MLP network.
Results in Table 2.
We observe that modeling object interactions leads to a 20% improvement in the RL success rate (i.e. 0 . 61 for MLP vs 0 . 804 for IN).
Impact of Decreasing Number of Demonstration Videos.
Results in Figure 6.
We ﬁnd that our approach is very data efﬁcient and can learn meaningful rewards even from a small number of videos.
It achieves decent RL success rate with only 10 % of total videos used (e.g. 72 % for Push).
Conclusions and Limitations
Conclusion.
We demonstrate the effectiveness of our proposed method, GraphIRL , in a number of IRL settings with diverse third-person demonstrations.
In particular, we show that our method successfully learns reward functions from human demonstrations with diverse objects and scene conﬁgurations, that we are able to train image-based policies in simulation using our learned rewards, and that policies trained with our learned rewards are more successful than both prior work and manually designed reward functions on a real robot.
We also hereby commit to release our complete code and data to the public. Limitations.
While our method relaxes the requirements for human demonstrations, collecting the demonstrations still requires human labor; and although our results indicate that we can learn from relatively few videos, eliminating human labor entirely remains an open problem. Moreover, our approach assumes access to object bounding boxes. This implies that our method’s performance is dependent on the performance of the object detector.
Fortunately, 2d object detectors have become very reliable as we show in our experiments, we are able to use an off-the-shelf object detector to extract the bounding boxes without having to perform any manual labeling.
Finally, the proposed graph abstraction allows us to solve tasks despite the large domain gap but it has some potential disadvantages too.
In particular, we lose ﬁne grained information such as object poses and precise object interactions which could be useful for complex tasks such as medical procedures.
However, we conjecture that 2D images might also not be sufﬁcient for such a task since inferring accurate object pose, 3D geometric information from a 2D image itself is a challenging problem.
Acknowledgments
This work was supported, in part, by grants from NSF CCF-2112665 (TILOS), NSF 1730158 CINew: Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI), NSF
ACI-1541349 CC*DNI Paciﬁc Research Platform, and gifts from Meta, Google, Qualcomm.
The authors would like to thank Sanjay Haresh, Kevin Zakka, Jianglong Ye and Mohit Jain for helpful discussions.
Appendix A Qualitative Analysis of Learned Reward
In this section, we present qualitative analysis of the reward learned using GraphIRL .
We plot the reward for GraphIRL and two baseline IRL methods for three test examples across three tasks.
The tasks we evaluate with are Peg in Box , Push , and Reach .
For each task, we use show two successful episodes and one unsuccessful episode.
The length of each episode is 50, and for each ﬁgure we have included, we provide images that align with critical points in the completion of the task.
[Figure]
[Figure]
[Figure]
[Figure]
[Figure]
[Figure]
We ﬁnd that our method provides a superior and accurate reward signal to the agent compared to the baseline visual IRL methods.
We observe that if a task is being completed successfully or unsuccessfully in a video, our method can obtain a reward that accurately reﬂects how close the agent is to completing the task.
Additionally, both XIRL and TCN yield low reward even for successful episodes due to large distance between the current observation and the representative goal observation in the embedding space which could be attributed to visual domain shift.
Appendix B Additional Implementation Details
Representation Learning.
Each MLP in the Spatial Interaction Encoder Network deﬁned in Equation 3.1 is implemented as a 2-layer network with a ReLU activation.
The size of the ﬁnal embedding ψ ( · ) is 128 in our experiments.
Please see Table 3 for a detailed list of hyperparameters for representation learning.
All the hyperparameters in Table 3 are kept ﬁxed for all tasks considered in this work.
Reinforcement Learning.
For X-MAGICAL, we follow Zakka et al.
[4] and learn a state based policy.
The state vector has dimensions of 16 and 17 for the Standard and Diverse environments
[Table]
respectively.
The Diverse environment state has an additional dimension to represent the size of blocks.
For xArm, we learn an image based policy.
Speciﬁcally, we use ﬁrst-person and third-person cameras to learn a policy from multi-view image data.
We extract 84 × 84 image from both cameras and concatenate them channel-wise.
We use the network architecture and attention mechanism proposed in Jangir et al.
Additionally, we apply data augmentation techniques: random ±pixel shift [58] and color jitter [59].
Extracting Reward.
In order to compute the reward during Reinforcement Learning (RL) training, we use the locations of objects available in simulation to extract the bounding boxes corresponding to the current observation.
The bounding boxes are used to construct the object representation which is then passed to the trained Spatial Interaction Encoder Network to get the reward.
Criterion for Success.
We use distance threshold to determine the success of an episode.
The thresholds are 5 cms, 10 cms and 8 cms for Reach , Push and Peg in Box respectively.
The distance refers to distance between goal position and end-effector for Reach , and goal position and object position for Push and Peg in Box .
Baseline Implementation Details.
For all the vision-based baselines, we use the hyperparameters, data augmentation schemes and network architectures provided in Zakka et al.
Readers are encouraged to read Zakka et al.
[4] for more details on the vision-based baselines.
Appendix C X-MAGICAL Experiment Details C.1 Demonstration Data
For collecting demonstration data in the X-MAGICAL Diverse environment, we trained 5 uniquelyseeded Soft Actor-Critic (SAC) RL policies for 2 million steps for each embodiment using the environment reward.
We collect 1000 successful episode rollouts for each embodiment using the 5 trained policies.
In particular, each policy is used to produce 200 episode rollouts for a given embodiment.
C.2 Diverse Environment
Below, we explain the randomization performed on the blocks in the diverse environment that we use in our experiments:
• Color: We randomly assign 1 out of 4 colors to each block.
• Shape: Each block is randomly assigned 1 out of 6 shapes.
• Size: The block sizes are also varied.
In particular, we generate a number between 0 . 75 and 1 .
and multiply the default block size by that factor.
• Initial Orientation: The initial orientation of the blocks is also randomized.
We randomly pick a value between 0 to 360 degrees.
• Initial Location: The initial location of the boxes is randomized by ﬁrst randomly picking a position for the y-coordinate for all blocks and then randomly selecting x-coordinate separately for each block.
This randomization is also performed in the standard environment.
[Figure]
[Figure]
Appendix D Additional Results on X-MAGICAL Benchmark
To complement our cross-embodiment cross-environment results from the main paper, we also report results for X-MAGICAL in the cross-embodiment same-environment setting.
As shown in Figure 13, we outperform TCN and LIFS by signiﬁcant margins and achieve comparable results to XIRL .
These results reﬂect the effectiveness of GraphIRL when learning in a visually similar environment with visually different agents.
Appendix E Appendix E: xArm Experiment Details E.1 Description of Environment Rewards
In this section, we deﬁne the environment rewards for xArm environments that were compared against GraphIRL in robot manipulation experiments under Section 4.
We deﬁne p g , p o , and p e as the positions of the goal, object and robot end-effector respectively.
The reward for Push is deﬁned as || p o − p g
|| 2 , for reach it becomes || p
e − p g
|| 2 and ﬁnally for Peg in Box , the reward is || p o − p
g
|| 2 .
Note that the distances are computed using 2-d positions in the case of Reach and Push and 3-d positions in the case of Peg in Box .
E.2 Demonstration Data
We use data from [22] for Push .
We collect 256 and 162 demonstrations respectively for Reach and Peg in Box .
For Reach , we use 18 visually distinct goal position markers i.e. 3 different shapes and each shape with 6 different colors in order to ensure visual diversity.
Reach demonstrations have minimum, average and maximum demonstration lengths of 1 .
76 seconds, 4 .
51 seconds and 9 .
23 seconds respectively.
For Peg in Box , we use 4 visually distinct objects.
In this case, the minimum, average and maximum demonstration lengths are 1 .
73 seconds, 4 .
74 seconds and 11 .seconds respectively.
For both Reach and Peg in Box , the goal and object positions are also varied across demonstrations to diversify trajectories.
Please see https://sateeshkumar21.github.
io/GraphIRL/ for examples of collected demonstrations.
Appendix F Impact of Decreasing Number of Demonstration Videos for Baselines
In Section 4.3, we show how decreasing number of demonstrations impacts performance for
GraphIRL .
For completeness, we repeat the same experiment for the vision-based baslines con-
[Figure]
sidered in this work
i
[Figure]
e. XIRL , TCN and LIFS .
Results in Figure 14.
We note that for Reach , XIRL ’s performance degrades signiﬁcantly with lesser number of demonstrations.
However, in other cases where the success rates are lower, we notice an inconsistent trend, indicating that vision-based baseline fail to learn meaningful representations regardless of the number of demonstrations.
Appendix G Additional Results on Robot Manipulation in Simulation
[Figure]
We also experiment with the MuJoCo State Pusher environment used by Schmeckpeper et al.
[22] and Zakka et al.
However, we make two changes, (1) Instead of using a ﬁxed goal position, we use a randomized goal position and learn a goal-conditioned policy and (2) we do not use the sparse environment reward and instead only use the learned rewards for GraphIRL and learning-based baselines.
Figure 15 presents our results, we note that GraphIRL achieves slightly lower success rate than the task-speciﬁc environment reward (e.g. GraphIRL 0 .
455 vs Environment Reward 0 . 6133 ).
Further, all vision-based baselines perform signiﬁcantly lower than GraphIRL (e.g. GraphIRL 0 .vs
XIRL 0 .
125 and TCN 0 .
For all learning-based methods, we use the data from Schmeckpeper et al.
[22] as training demonstrations similar to Push experiments conducted in Section 4.
[Figure]
Appendix H Robot Setup
We use a Ufactory xArm 7 robot for our real robot experiments.
As shown in Figure 16, we use a ﬁxed third-person camera and an egocentric camera that is attached above the robot’s gripper.
Example images of the egocentric and third-person camera feeds passed to the RL agent are shown in Figure 16 (c) and Figure 16 (d).