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Title: Deep Imitative Models for Flexible Inference, Planning, and Control

Paper content:
Imitation Learning (IL) is an appealing approach to learn desirable autonomous behavior.
However, directing IL to achieve arbitrary goals is difficult.
In contrast, planning-based algorithms use dynamics models and reward functions to achieve goals.
Yet, reward functions that evoke desirable behavior are often difficult to specify.
In this paper, we propose "Imitative Models" to combine the benefits of IL and goal-directed planning.
Imitative Models are probabilistic predictive models of desirable behavior able to plan interpretable expert-like trajectories to achieve specified goals.
We derive families of flexible goal objectives, including constrained goal regions, unconstrained goal sets, and energy-based goals.
We show that our method can use these objectives to successfully direct behavior.
Our method substantially outperforms six IL approaches and a planning-based approach in a dynamic simulated autonomous driving task, and is efficiently learned from expert demonstrations without online data collection.
We also show our approach is robust to poorly-specified goals, such as goals on the wrong side of the road.
Imitation learning (IL) is a framework for learning a model to mimic behavior.
At test-time, the model pursues its best-guess of desirable behavior.
By letting the model choose its own behavior, we cannot direct it to achieve different goals.
While work has augmented IL with goal conditioning (Dosovitskiy & Koltun, 2016; Codevilla et al., 2018) , it requires goals to be specified during training, explicit goal labels, and are simple (e.g., turning).
In contrast, we seek flexibility to achieve general goals for which we have no demonstrations.
In contrast to IL, planning-based algorithms like model-based reinforcement learning (MBRL) methods do not require expert demonstrations.
MBRL can adapt to new tasks specified through reward functions (Kuvayev & Sutton, 1996; Deisenroth & Rasmussen, 2011) .
The "model" is a dynamics model, used to plan under the user-supplied reward function.
Planning enables these approaches to perform new tasks at test-time.
The key drawback is that these models learn dynamics of possible behavior rather than dynamics of desirable behavior.
This means that the responsibility of evoking desirable behavior is entirely deferred to engineering the input reward function.
Designing reward functions that cause MBRL to evoke complex, desirable behavior is difficult when the space of possible undesirable behaviors is large.
In order to succeed, the rewards cannot lead the model astray towards observations significantly different than those with which the model was trained.
Our goal is to devise an algorithm that combines the advantages of MBRL and IL by offering MBRL's flexibility to achieve new tasks at test-time and IL's potential to learn desirable behavior entirely from offline data.
To accomplish this, we first train a model to forecast expert trajectories with a density function, which can score trajectories and plans by how likely they are to come from the expert.
A probabilistic model is necessary because expert behavior is stochastic: e.g. at an intersection, the expert could choose to turn left or right.
Next, we derive a principled probabilistic inference objective to create plans that incorporate both (1) the model and (2) arbitrary new tasks.
Finally, we derive families of tasks that we can provide to the inference framework.
Our method can accomplish new tasks specified as complex goals without having seen an expert complete these tasks before.
We investigate properties of our method on a dynamic simulated autonomous driving task (see Fig. 1 ).
Videos are available at https://sites.google.com/view/imitative-models.
Our contributions are as follows:
Figure 1: Our method: deep imitative models.
Top Center.
We use demonstrations to learn a probability density function q of future behavior and deploy it to accomplish various tasks.
Left: A region in the ground plane is input to a planning procedure that reasons about how the expert would achieve that task.
It coarsely specifies a destination, and guides the vehicle to turn left.
Right: Goal positions and potholes yield a plan that avoids potholes and achieves one of the goals on the right.
1. Interpretable expert-like plans with minimal reward engineering.
Our method outputs multistep expert-like plans, offering superior interpretability to one-step imitation learning models.
In contrast to MBRL, our method generates expert-like behaviors with minimal reward engineering.
2. Flexibility to new tasks: In contrast to IL, our method flexibly incorporates and achieves goals not seen during training, and performs complex tasks that were never demonstrated, such as navigating to goal regions and avoiding test-time only potholes, as depicted in Fig. 1 .
3. Robustness to goal specification noise: We show that our method is robust to noise in the goal specification.
In our application, we show that our agent can receive goals on the wrong side of the road, yet still navigate towards them while staying on the correct side of the road.
4. State-of-the-art CARLA performance: Our method substantially outperforms MBRL, a custom IL method, and all five prior CARLA IL methods known to us.
It learned near-perfect driving through dynamic and static CARLA environments from expert observations alone.
We proposed "Imitative Models" to combine the benefits of IL and MBRL.
Imitative Models are probabilistic predictive models able to plan interpretable expert-like trajectories to achieve new goals.
Inference with an Imitative Model resembles trajectory optimization in MBRL, enabling it to both incorporate new goals and plan to them at test-time, which IL cannot.
Learning an Imitative Model resembles offline IL, enabling it to circumvent the difficult reward-engineering and costly online data collection necessities of MBRL.
We derived families of flexible goal objectives and showed our model can successfully incorporate them without additional training.
Our method substantially outperformed six IL approaches and an MBRL approach in a dynamic simulated autonomous driving task.
We showed our approach is robust to poorly specified goals, such as goals on the wrong side of the road.
We believe our method is broadly applicable in settings where expert demonstrations are available, flexibility to new situations is demanded, and safety is paramount.
Future work could investigate methods to handle both observation noise and out-of-distribution observations to enhance the applicability to robust real systems -we expand on this issue in Appendix E. Finally, to facilitate more general planning, future work could extend our approach to explicitly reason about all agents in the environment in order to inform a closed-loop plan for the controlled agent.

assistant: text: In this paper, we propose Imitative Models to combine the benefits of IL and goal-directed planning: probabilistic predictive models of desirable behavior able to plan interpretable expert-like trajectories to achieve specified goals.