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Title: Meta-learning curiosity algorithms

Paper content:
Exploration is a key component of successful reinforcement learning, but optimal approaches are computationally intractable, so researchers have focused on hand-designing mechanisms based on exploration bonuses and intrinsic reward, some inspired by curious behavior in natural systems.
In this work, we propose a strategy for encoding curiosity algorithms as programs in a domain-specific language and searching, during a meta-learning phase, for algorithms that enable RL agents to perform well in new domains.
Our rich language of programs, which can combine neural networks with other building blocks including nearest-neighbor modules and can choose its own loss functions, enables the expression of highly generalizable programs that perform well in domains as disparate as grid navigation with image input, acrobot, lunar lander, ant and hopper.
To  make this approach feasible, we develop several pruning techniques, including learning to predict a program's success based on its syntactic properties.
We demonstrate the effectiveness of the approach empirically, finding curiosity strategies that are similar to those in published literature, as well as novel strategies that are competitive with them and generalize well.
Figure 1: Our RL agent is augmented with a curiosity module, obtained by meta-learning over a complex space of programs, which computes a pseudo-reward r at every time step.
When an agent is learning to behave online, via reinforcement learning (RL), it is critical that it both explores its domain and exploits its rewards effectively.
In very simple problems, it is possible to solve the problem optimally, using techniques of Bayesian decision theory (Ghavamzadeh et al., 2015) .
However, these techniques do not scale at all well and are not effectively applicable to the problems addressable by modern deep RL, with large state and action spaces and sparse rewards.
This difficulty has left researchers the task of designing good exploration strategies for RL systems in complex environments.
One way to think of this problem is in terms of curiosity or intrisic motivation: constructing reward signals that augment or even replace the extrinsic reward from the domain, which induce the RL agent to explore their domain in a way that results in effective longer-term learning and behavior (Pathak et al., 2017; Burda et al., 2018; Oudeyer, 2018) .
The primary difficulty with this approach is that researchers are hand-designing these strategies: it is difficult for humans to systematically consider the space of strategies or to tailor strategies for the distribution of environments an agent might be expected to face.
We take inspiration from the curious behavior observed in young humans and other animals and hypothesize that curiosity is a mechanism found by evolution that encourages meaningful exploration early in agent's life in order to expose it to experiences that enable it to learn to obtain high rewards over the course of its lifetime.
We propose to formulate the problem of generating curious behavior as one of meta-learning: an outer loop, operating at "evolutionary" scale will search over a space of algorithms for generating curious behavior by dynamically adapting the agent's reward signal, and the inner loop will perform standard reinforcement learning using the adapted reward signal.
This process is illustrated in figure 1; note that the aggregate agent, outlined in gray, has the standard interface of an RL agent.
The inner RL algorithm is continually adapting to its input stream of states and rewards, attempting to learn a policy that optimizes the discounted sum of proxy rewards k≥0 γ k r t+k .
The outer "evolutionary" search is attempting to find a program for the curiosity module, so to optimize the agent's lifetime return T t=0 r t , or another global objective like the mean performance on the last few trials.
Although it is, in principle, possible to discover a complete, integrated algorithm for the entire curious learning agent in the gray box, that is a much more complex search problem that is currently computationally infeasible.
We are relying on the assumption that the foundational methods for reinforcement learning, including those based on temporal differencing and policy gradient, are fundamentally sound and can serve as the behavior-learning basis for our agents.
It is important to note, though, that the internal RL algorithm in our architecture must be able to tolerate a nonstationary reward signal, which may necessitate minor algorithmic changes or, at least, different hyperparameter values.
In this meta-learning setting, our objective is to find a curiosity module that works well given a distribution of environments from which we can sample at meta-learning time.
If the environment distribution is relatively low-variance (the tasks are all quite similar) then it might suffice to search over a relatively simple space of curiosity strategies (most trivially, the in an -greedy exploration strategy).
Meta-RL has been widely explored recently, in some cases with a focus on reducing the amount of experience needed by initializing the RL algorithm well (Finn et al., 2017; Clavera et al., 2019) and, in others, for efficient exploration (Duan et al., 2016; Wang et al., 2017) .
The environment distributions in these cases have still been relatively low-diversity, mostly limited to variations of the same task, such as exploring different mazes or navigating terrains of different slopes.
We would like to discover curiosity mechanisms that can generalize across a much broader distribution of environments, even those with different state and action spaces: from image-based games, to joint-based robotic control tasks.
To do that, we perform meta-learning in a rich, combinatorial, open-ended space of programs.
This paper makes three novel contributions.
We focus on a regime of meta-reinforcement-learning in which the possible environments the agent might face are dramatically disparate and in which the agent's lifetime is very long.
This is a substantially different setting than has been addressed in previous work on meta-RL and it requires substantially different techniques for representation and search.
We represent meta-learned curiosity strategies in a rich, combinatorial space of programs rather than in a fixed-dimensional numeric parameter space.
The programs are represented in a domain-specific language (DSL) which includes sophisticated building blocks including neural networks complete with gradient-descent mechanisms, learned objective functions, ensembles, buffers, and other regressors.
This language is rich enough to represent many previously reported hand-designed exploration algorithms.
We believe that by performing meta-RL in such a rich space of mechanisms, we will be able to discover highly general, fundamental curiosity-based exploration methods.
This generality means that a relatively computationally expensive meta-learning process can be amortized over the lifetimes of many agents in a wide variety of environments.
We make the search over programs feasible with relatively modest amounts of computation.
It is a daunting search problem to find a good solution in a combinatorial space of programs, where evaluating a single potential solution requires running an RL algorithm for up to millions of time steps.
We address this problem in multiple ways.
By including environments of substantially different difficulty and character, we can evaluate candidate programs first on relatively simple and short-horizon domains: if they don't perform well in those domains, they are pruned early, which saves a significant amount of computation time.
In addition, we predict the performance of an algorithm from its structure and operations, thus trying the most promising algorithms early in our search.
Finally, we also monitor the learning curve of agents and stop unpromising programs before they reach all T environment steps.
We demonstrate the effectiveness of the approach empirically, finding curiosity strategies that are similar to those in published literature, as well as novel strategies that are competitive with them and generalize well.
In this work we show that programs are a powerful, succinct, representation for algorithms for generating curious exploration, and these programs can be meta-learned efficiently via active search.
Results from this work are two-fold.
First, by construction, algorithms resulting from this search will have broad generalization and will thus be a useful default for RL settings, where reliability is key.
Second, the algorithm search code will be open-sourced to facilitate further research on exploration algorithms based on new ideas or building blocks, which can be added to the search.
In addition, we note that the approach of meta-learning programs instead of network weights may have further applications beyond finding curiosity algorithms, such as meta-learning optimization algorithms or even meta-learning meta-learning algorithms.

assistant: text: Meta-learning curiosity algorithms by searching through a rich space of programs yields novel mechanisms that generalize across very different reinforcement-learning domains.