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Title: Novelty Search in representational space for sample efficient exploration

Paper content:
We present a new approach for efficient exploration which leverages a low-dimensional encoding of the environment learned with a combination of model-based and model-free objectives.
Our approach uses intrinsic rewards that are based on a weighted distance of nearest neighbors in the low dimensional representational space to gauge novelty.
We then leverage these intrinsic rewards for sample-efficient exploration with planning routines in representational space.
One key element of our approach is that we perform more gradient steps in-between every environment step in order to ensure the model accuracy.
We test our approach on a number of maze tasks, as well as a control problem and show that our exploration approach is more sample-efficient compared to strong baselines.
In order to solve a task efficiently in Reinforcement Learning (RL), one of the main challenges is to gather informative experiences thanks to an efficient exploration of the state space.
A common approach to exploration is intrinsic rewards correlated with some novelty heuristics (Schmidhuber, 2010; Houthooft et al., 2016) .
With intrinsic rewards, an agent can be incentivized to efficiently explore its state space.
A direct approach to calculating these novelty heuristics is to derive a reward based on the observations, such as a count-based reward (Bellemare et al., 2016; Ostrovski et al., 2017) or a prediction-error based reward (Burda et al., 2018b) .
However, an issue occurs when measuring novelty directly from the raw observations, as some information in the pixel space (such as randomness) might be irrelevant.
In this case, if an agent wants to efficiently explore its state space it should only focus on meaningful and novel information.
In this work, we propose a method of sample-efficient exploration by leveraging novelty heuristics in a meaningful abstract state space.
We leverage a low-dimensional abstract representation of states, which is learned by fitting both model-based and model-free components through a joint representation.
This provides a meaningful abstract representation where states that are close temporally in dynamics are brought close together in low-dimensional representation space.
We also add additional constraints to ensure that a measure of distance between states is meaningful.
With this distance in representational space, we form a novelty heuristic inspired by the Novelty Search algorithm (Lehman and Stanley, 2011) to generate intrinsic rewards that we use for efficient exploration.
We show that with a good low-dimensional representation of states, a policy based on planning with our novelty heuristic is able to explore with high sample-efficiency.
In our experiments, we measure the effectiveness of our exploration methods by the number of samples required to explore the state space.
One key element of our approach is that we perform more gradient steps in-between every environment step in order to ensure the model accuracy is high (and hence ensure an accurate novelty heuristic).
Through this training scheme, our agent is also able to learn a meaningful representation of its state space in an extremely sample-efficient manner.
In this paper, we show that with an interpretable abstract representation of states, our novelty metric is able to serve as an intrinsic reward that enables efficient exploration.
By using this novelty metric with a combination of model-based and model-free approaches for planning, we demonstrate the efficiency of our method in multiple environments.
As with most methods, our approach also has limitations.
While the problem of distance metrics in high-dimensional space is partially solved in our method with the dimensionality reduction of observations by our encoder, the 2 -norm still requires a low dimension to be useful (Aggarwal et al., 2002) .
This implies that our novelty metric may lose its effectiveness as we increase the dimension of our abstract representation.
In addition, our exploration strategy benefits greatly from the meaningful abstractions and internal model.
In some cases, the model can over-generalize with the consequence that the low-dimensional representation loses information that is crucial for the exploration of the entire state space.
An interesting direction for future work would be find ways of incorporating the secondary features mentioned in Section 6.1.2.
A DISCUSSION ON THE ENTROPY CONSTRAINT As for our soft constraints on representation magnitude, we use a local constraint instead of a global constraint on magnitude such that it is more suited for our novelty metric.
If we are to calculate some form of intrinsic reward based on distance between neighboring states, then this distance needs to be non-zero and ideally consistent as the number of states in our history increases.
In the global constraint case, if the intrinsic rewards decreases with an increase in number of states in the agent's history, then the agent will fail to be motivated to explore further.
Even though the entropy maximization losses ensures the maximization of distances between random states, if we have |H s | number of states in the history of the agent, then a global constraint on representation magnitude might lead to lim Here H s is a list of all possible states in S in any order, with each possible state appearing only once.
If we let k = 4, we have that:
While it may seem redundant to include the 1st nearest neighbor distance in this metric (which would be itself if we've visited the state), the 1st nearest neighbor is non-zero when we calculate the novelty of a predicted state using our learned transition functionτ .
From this example, we can see that there is a bias towards states with fewer direct neighbors due to the nature of our novelty metric.
This poses an issue -if our goal is for sample-efficient exploration of our state space, then there is no reason to favor states with less direct neighbors.

assistant: text: We conduct exploration using intrinsic rewards that are based on a weighted distance of nearest neighbors in representational space.