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Title: Directed-Info GAIL: Learning Hierarchical Policies from Unsegmented Demonstrations using Directed Information

Paper content:
The use of imitation learning to learn a single policy for a complex task that has multiple modes or hierarchical structure can be challenging.
In fact, previous work has shown that when the modes are known, learning separate policies for each mode or sub-task can greatly improve the performance of imitation learning.
In this work, we discover the interaction between sub-tasks from their resulting state-action trajectory sequences using a directed graphical model.
We propose a new algorithm based on the generative adversarial imitation learning framework which automatically learns sub-task policies from unsegmented demonstrations.
Our approach maximizes the directed information flow in the graphical model between sub-task latent variables and their generated trajectories.
We also show how our approach connects with the existing Options framework, which is commonly used to learn hierarchical policies.
Complex human activities can often be broken down into various simpler sub-activities or sub-tasks that can serve as the basic building blocks for completing a variety of complicated tasks.
For instance, when driving a car, a driver may perform several simpler sub-tasks such as driving straight in a lane, changing lanes, executing a turn and braking, in different orders and for varying times depending on the source, destination, traffic conditions etc.
Using imitation learning to learn a single monolithic policy to represent a structured activity can be challenging as it does not make explicit the sub-structure between the parts within the activity.
In this work, we develop an imitation learning framework that can learn a policy for each of these sub-tasks given unsegmented activity demonstrations and also learn a macro-policy which dictates switching from one sub-task policy to another.
Learning sub-task specific policies has the benefit of shared learning.
Each such sub-task policy also needs to specialize over a restricted state space, thus making the learning problem easier.Previous works in imitation learning BID16 BID7 focus on learning each sub-task specific policy using segmented expert demonstrations by modeling the variability in each sub-task policy using a latent variable.
This latent variable is inferred by enforcing high mutual information between the latent variable and expert demonstrations.
This information theoretic perspective is equivalent to the graphical model shown in FIG0 (Left), where the node c represents the latent variable.
However, since learning sub-task policies requires isolated demonstrations for each sub-task, this setup is difficult to scale to many real world scenarios where providing such segmented trajectories is cumbersome.
Further, this setup does not learn a macro-policy to combine the learned sub-task policies in meaningful ways to achieve different tasks.In our work, we aim to learn each sub-task policy directly from unsegmented activity demonstrations.
For example, given a task consisting of three sub-tasks -A, B and C, we wish to learn a policy to complete sub-task A, learn when to transition from A to B, finish sub-task B and so on.
To achieve this we use a causal graphical model, which can be represented as a Dynamic Bayesian Network as GAIL Li et al. (2017) .
Right: Causal model in this work.
The latent code causes the policy to produce a trajectory.
The current trajectory, and latent code produce the next latent code shown in FIG0 (Right).
The nodes c t denote latent variables which indicate the currently active sub-task and the nodes τ t denote the state-action pair at time t.
We consider as given, a set of expert demonstrations, each of which is represented by τ = {τ 1 , · · · , τ T } and has a corresponding sequence of latent factors c = {c 1 , · · · , c T −1 }.
The sub-activity at time t dictates what state-action pair was generated at time t.
The previous sub-task and the current state together cause the selection of the next sub-task.As we will discuss in Section 3, extending the use of mutual information to learn sub-task policies from unsegmented demonstrations is problematic, as it requires learning the macro-policy as a conditional probability distribution which depends on the unobserved future.
This unobserved future is unknown during earlier points of interaction ( FIG0 ).
To alleviate this, in our work we aim to force the policy to generate trajectories that maximize the directed information or causal information BID17 flow from trajectories to latent factors of variation within the trajectories instead of mutual information.
Using directed information requires us to learn a causally conditioned probability distribution BID12 which depends only on the observed past while allowing the unobserved future to be sequentially revealed.
Further, since there exists feedback in our causal graphical model i.e., information flows from the latent variables to trajectories and vice versa, directed information also provides a better upper bound on this information flow between the latent variables and expert trajectories than does the conventional mutual information BID17 BID12 .We
also draw connections with existing work on learning sub-task policies using imitation learning with the options framework BID27 BID3 . We
show that our work, while derived using the information theoretic perspective of maximizing directed information, bears a close resemblance to applying the options framework in a generative adversarial imitation setting. Thus
, our approach combines the benefits of learning hierarchical policies using the options framework with the robustness of generative adversarial imitation learning, helping overcome problems such as compounding errors that plague behaviour cloning.In summary, the main contributions of our work include:• We extend existing generative adversarial imitation learning frameworks to allow for learning of sub-task specific policies by maximizing directed information in a causal graph of subactivity latent variables and observed trajectory variables.• We
draw connections between previous works on imitation learning with sub-task policies using options and show that our proposed approach can also be seen as option learning in a generative adversarial setting.• We
show through experiments on both discrete and continuous state-action spaces, the ability of our approach to segment expert demonstrations into meaningful sub-tasks and combine sub-task specific policies to perform the desired task.2 RELATED
WORK
Learning separate sub-task policies can help improve the performance of imitation learning when the demonstrated task is complex and has a hierarchical structure.
In this work, we present an algorithm that infers these latent sub-task policies directly from given unstructured and unlabelled expert demonstrations.
We model the problem of imitation learning as a directed graph with sub-task latent variables and observed trajectory variables.
We use the notion of directed information in a generative adversarial imitation learning framework to learn sub-task and macro policies.
We further show theoretical connections with the options literature as used in hierarchical reinforcement and imitation learning.
We evaluate our method on both discrete and continuous environments.
Our experiments show that our method is able to segment the expert demonstrations into different sub-tasks, learn sub-task specific policies and also learn a macro-policy that can combines these sub-task.
TAB3 : Experiment settings for all the different environments for both DirectedInfo-GAIL and VAE-pretraining step respectively.
Thus, by maximizing directed information instead of mutual information, we can learn a posterior distribution over the next latent factor c given the latent factors discovered up to now and the trajectory followed up to now, thereby removing the dependence on the future trajectory.
In practice, we do not consider the H(c) term.
This gives us the objective, DISPLAYFORM0 In practice, we fix q from the VAE pre-training and only minimize over the policy π in equation 4.
BID24 to train our policy network with = 0.2.
For the VAE pre-training step we set the VAE learning rate also to 3e −4 .
For the Gumbel-Softmax distribution we set an initial temperature τ = 5.0.
The temperature is annealed using using an exponential decay with the following schedule τ = max(0.1, exp −kt ), where k = 3e − 3 and t is the current epoch.

assistant: text: Learning Hierarchical Policies from Unsegmented Demonstrations using Directed Information