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Proximal Policy Optimization with Continuous Bounded Action Space via the Beta Distribution

on Fri, 11/04/2022 - 21:38

Reinforcement learning methods for continuous control tasks have evolved in recent years generating a family of policy gradient methods that rely primarily on a Gaussian distribution for modeling a stochastic policy. However, the Gaussian distribution has an infinite support, whereas real world applications usually have a bounded action space. This dissonance causes an estimation bias that can be eliminated if the Beta distribution is used for the policy instead, as it presents a finite support. In this work, we investigate how this Beta policy performs when it is trained by the Proximal Policy Optimization (PPO) algorithm on two continuous control tasks from OpenAI gym. For both tasks, the Beta policy is superior to the Gaussian policy in terms of agent's final expected reward, also showing more stability and faster convergence of the training process. For the CarRacing environment with high-dimensional image input, the agent's success rate was improved by 63% over the Gaussian policy.

The CarRacing-v0 environment simulates an autonomous driving environment in 2D.

The observation space consists of top down images of 96x96 pixels and three (RGB) color channels. The latest four image frames were stacked and given as input to the agent's network after rescaling and preprocessing them to gray scale (totalling 84x84x4 input dimensions).
The action space has three dimensions: one encodes the steering angle and is bounded in the interval [-1, +1]. The other two dimensions encode throttle and brake, both bounded to [0, 1]. 

In the plot below, we can see the average rewards for 5 agents with different seeds for the CarRacing environment.
The final performance is shown on the bottom plots at a bigger scale, for agents with Gaussian policy (bottom left) and Beta policy (bottom right). 

Next, we see an illustration of the Gaussian and Beta stochastic policy distributions in relation to the action space of the CarRacing environment. 
For a fixed observation s (preprocessed image in left plot), we sampled the Gaussian and Beta policies for 5000 actions. 
For the Gaussian distribution, a significant portion of the actions fall out of the valid direction and brake/throttle range (both [-1, 1]), whereas for the Beta distributions, all actions fall within boundaries.


OpenAI CarRacing-v0 Leaderboard hosts a series of self-reported scores. We compare our results only to those found in peer-reviewed articles since they provide a basis for comparison and discussion.
Our proposal currently (as of 2021) surpass state-of-the-art models, beating all work reported previously in the literature.





Generative Adversarial Imitation Learning for End-to-End Autonomous Driving on Urban Environments

on Fri, 11/04/2022 - 20:35

Autonomous driving is a complex task, which has been tackled since the first self-driving car ALVINN in 1989, with a supervised learning approach, or behavioral cloning (BC). In BC, a neural network is trained with state-action pairs that constitute the training set made by an expert, i.e., a human driver. However, this type of imitation learning does not take into account the temporal dependencies that might exist between actions taken in different moments of a navigation trajectory. These type of tasks are better handled by reinforcement learning (RL) algorithms, which need to define a reward function. On the other hand, more recent approaches to imitation learning, such as Generative Adversarial Imitation Learning (GAIL), can train policies without explicitly requiring to define a reward function, allowing an agent to learn by trial and error directly on a training set of expert trajectories. % In this work, we propose two variations of GAIL for autonomous navigation of a vehicle in the realistic CARLA simulation environment for urban scenarios. Both of them use the same network architecture, which process high-dimensional image input from three frontal cameras, and other nine continuous inputs representing the velocity, the next point from the sparse trajectory and a high-level driving command. We show that both of them are capable of imitating the expert trajectory from start to end after training ends, but the GAIL loss function that is augmented with BC outperforms the former in terms of convergence time and training stability.

Images from the three frontal cameras located at the left, central, and right part of the vehicle, respectively. They were taken after the first few interactions of the agent in the CARLA simulation environment considering our defined trajectory. Each camera produces a RGB image with 144 pixels of height and 256 pixels of width. These images are fed to the networks as they are.


Architecture of the actor-critic network and discriminator - each of them has its own separate network, with the latter having an additional input for the action, in orange color, and a sigmoidal output $D(s,a)$ instead of the output layer of the actor-critic network which consists of the steering direction, throttle as actions for the actor (policy) and value of the current state $V(s)$ for the critic. The common, though not shared architecture (in blue) is composed of a convolutional block that process the images of the three frontal cameras, whose output features are concatenated with other nine continuous inputs for speed, next target point in the sparse GPS trajectory, and a high-level driving command. The resulting feature vector is input to a block of two fully-connected (FC) layers.

Average rewards vs environment interactions during training in the long route (setup 2). For each method (GAIL and GAIL with BC), the average performance of two runs (i.e, two agents trained from scratch) is shown with a stochastic policy (left plot) and a deterministic policy (right plot). The shaded area represents the standard deviation. The behavior cloning (BC) attains an average reward of 173.6 for ten episodes, while the maximum is at 760, achieved by both GAIL and GAIL augmented with BC.




Generative Modeling of Autonomous Robots and their Environments using Reservoir Computing

on Wed, 01/20/2016 - 21:02

Autonomous mobile robots form an important research topic in the field of robotics due to their near-term applicability in the real world as domestic service robots. These robots must be designed in an efficient way using training sequences. They need to be aware of their position in the environment and also need to create models of it for deliberative planning. These tasks have to be performed using a limited number of sensors with low accuracy, as well as with a restricted amount of computational power. In this contribution we show that the recently emerged paradigm of Reservoir Computing (RC) is very well suited to solve all of the above mentioned problems, namely learning by example, robot localization, map and path generation. Reservoir Computing is a technique which enables a system to learn any time-invariant filter of the input by training a simple linear regressor that acts on the states of a highdimensional but random dynamic system excited by the inputs. In addition, RC is a simple technique featuring ease of training, and low computational and memory demands.

Keywords: reservoir computing, generative modeling, map learning, T-maze task, road sign problem, path generation







Related Publications

  1. Eric AntoneloBenjamin Schrauwen and Jan Van Campenhout Generative Modeling of Autonomous Robots and their Environments using Reservoir Computing Neural Processing Letters, Vol. 26(3), pp. 233-249 (2007)