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Title: Robust Domain Randomization for Reinforcement Learning

Paper content:
Producing agents that can generalize to a wide range of environments is a significant challenge in reinforcement learning.
One method for overcoming this issue is domain randomization, whereby at the start of each training episode some parameters of the environment are randomized so that the agent is exposed to many possible variations.
However, domain randomization is highly inefficient and may lead to policies with high variance across domains.
In this work, we formalize the domain randomization problem, and show that minimizing the policy's Lipschitz constant with respect to the randomization parameters leads to low variance in the learned policies.
We propose a method where the agent only needs to be trained on one variation of the environment, and its learned state representations are regularized during training to minimize this constant.
We conduct experiments that demonstrate that our technique leads to more efficient and robust learning than standard domain randomization, while achieving equal generalization scores.
Deep Reinforcement Learning (RL) has proven very successful on complex high-dimensional problems ranging from games like Go (Silver et al., 2017) and Atari games (Mnih et al., 2015) to robot control tasks .
However, one prominent issue is that of overfitting, illustrated in figure 1: agents trained on one domain fail to generalize to other domains that differ only in small ways from the original domain (Sutton, 1996; Cobbe et al., 2018; Zhang et al., 2018b; Packer et al., 2018; Zhang et al., 2018a; Witty et al., 2018; Farebrother et al., 2018) .
Good generalization is essential for problems such as robotics and autonomous vehicles, where the agent is often trained in a simulator and is then deployed in the real world where novel conditions will certainly be encountered.
Transfer from such simulated training environments to the real world is known as crossing the reality gap in robotics, and is well known to be difficult, thus providing an important motivation for studying generalization.
We focus on the problem of generalizing between environments that visually differ from each other, for example in color or texture, but where the underlying dynamics are the same.
In reinforcement learning, prior work to address this topic has studied both domain adaptation and domain randomization.
Domain adaptation techniques aim to update the data distribution in simulation to match the real distribution through some form of canonical mapping or using regularization methods (James et al., 2018; Bousmalis et al., 2017; Gamrian & Goldberg, 2018) .
Alternatively, domain randomization, in which the visual and physical properties of the training domains are randomized at the start of each episode during training, has also been shown to lead to improved generalization and transfer to the real world with little or no real world data (Tobin et al., 2017; Sadeghi & Levine, 2016; Antonova et al., 2017; Peng et al., 2017; Mordatch et al., 2015; Rajeswaran et al., 2016; OpenAI, 2018) .
However, domain randomization has been empirically shown to often lead to suboptimal policies with high variance in performance over different randomizations (Mehta et al., 2019) .
This issue can cause the learned policy to underperform in any given target domain.
We propose a regularization method for learning policies that are robust to irrelevant visual changes in the environment.
Our work combines aspects from both domain adaptation and domain randomization, in that we maintain the notion of randomized environments but use a regularization method to achieve good generalization over the randomization space.
Our contributions are the following:
• We formalize the visual domain randomization problem, and show that the Lipschitz constant of the agent's policy over visual variations provides an upper bound on the agent's robustness to these variations.
• We propose an algorithm whereby the agent is only trained on one variation of the environment but its learned representations are regularized so that the Lipschitz constant is minimized.
• We experimentally show that our method is more efficient and leads to lower-variance policies than standard domain randomization, while achieving equal or better returns and generalization ability.
This paper is structured as follows.
We first review related work, formalize the visual generalization problem, and present our theory contributions.
We then describe our regularization method, and illustrate its application to a toy gridworld problem.
Finally, we compare our method with standard domain randomization and other regularization techniques in complex visual environments.
Figure 1: Illustration of the visual generalization challenge in reinforcement learning.
In this cartpole domain, the agent must learn to keep the pole upright.
However, changes in the background color can completely throw off a trained agent.
In this paper we studied generalization to visually diverse environments in deep reinforcement learning.
We formalized the problem, illustrated the inefficiencies of standard domain randomization, and proposed a theoretically grounded method that leads to robust, low-variance policies that generalize well.
We conducted several experiments in different environments of differing complexities using both on-policy and off-policy algorithms to support our claims.

assistant: text: We produce reinforcement learning agents that generalize well to a wide range of environments using a novel regularization technique.