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Title: Fast Task Inference with Variational Intrinsic Successor Features

Paper content:
It has been established that diverse behaviors spanning the controllable subspace of a Markov decision process can be trained by rewarding a policy for being distinguishable from other policies.
However, one limitation of this formulation is the difficulty to generalize beyond the finite set of behaviors being explicitly learned, as may be needed in subsequent tasks.
Successor features provide an appealing solution to this generalization problem, but require defining the reward function as linear in some grounded feature space.
In this paper, we show that these two techniques can be combined, and that each method solves the other's primary limitation.
To do so we introduce Variational Intrinsic Successor FeatuRes (VISR), a novel algorithm which learns controllable features that can be leveraged to provide enhanced generalization and fast task inference through the successor features framework.
We empirically validate VISR on the full Atari suite, in a novel setup wherein the rewards are only exposed briefly after a long unsupervised phase.
Achieving human-level performance on 12 games and beating all baselines, we believe VISR represents a step towards agents that rapidly learn from limited feedback.
Unsupervised learning has played a major role in the recent progress of deep learning.
Some of the earliest work of the present deep learning era posited unsupervised pre-training as a method for overcoming optimization difficulties inherent in contemporary supervised deep neural networks (Hinton et al., 2006; Bengio et al., 2007) .
Since then, modern deep neural networks have enabled a renaissance in generative models, with neural decoders allowing for the training of large scale, highly expressive families of directed models (Goodfellow et al., 2014; Van den Oord et al., 2016) as well as enabling powerful amortized variational inference over latent variables (Kingma and Welling, 2013) .
We have repeatedly seen how representations from unsupervised learning can be leveraged to dramatically improve sample efficiency in a variety of supervised learning domains (Rasmus et al., 2015; Salimans et al., 2016) .
In the reinforcement learning (RL) setting, the coupling between behavior, state visitation, and the algorithmic processes that give rise to behavior complicate the development of "unsupervised" methods.
The generation of behaviors by means other than seeking to maximize an extrinsic reward has long been studied under the psychological auspice of intrinsic motivation (Barto et al., 2004; Barto, 2013; Mohamed and Rezende, 2015) , often with the goal of improved exploration (Şimşek and Barto, 2006; Oudeyer and Kaplan, 2009; Bellemare et al., 2016) .
However, while exploration is classically concerned with the discovery of rewarding states, the acquisition of useful state representations and behavioral skills can also be cast as an unsupervised (i.e. extrinsically unrewarded) learning problem for agents interacting with an environment.
In the traditional supervised learning setting, popular classification benchmarks have been employed (with labels removed) as unsupervised representation learning benchmarks, wherein the acquired representations are evaluated based on their usefulness for some downstream task (most commonly the original classification task with only a fraction of the labels reinstated).
Analogously, we propose removing the rewards from an RL benchmark environment for unsupervised pre-training of an agent, with their subsequent reinstatement testing for dataefficient adaptation.
This setup emulates scenarios where unstructured interaction with the environment, or a closely related environment, is relatively inexpensive to acquire and the agent is expected to perform one or more tasks defined in this environment in the form of rewards.
The current state-of-the-art for RL with unsupervised pre-training comes from a class of algorithms which, independent of reward, maximize the mutual information between latent variable policies and their behavior in terms of state visitation, an objective which we refer to as behavioral mutual information (Mohamed and Rezende, 2015; Gregor et al., 2016; Eysenbach et al., 2018; Warde-Farley et al., 2018) .
These objectives yield policies which exhibit a great deal of diversity in behavior, with variational intrinsic control (Gregor et al., 2016, VIC) and diversity is all you need (Eysenbach et al., 2018, DIAYN) even providing a natural formalism for adapting to the downstream RL problem.
However, both methods suffer from poor generalization and a slow inference process when the reward signal is introduced.
The fundamental problem faced by these methods is the requirement to effectively interpolate between points in the latent behavior space, as the most task-appropriate latent skill likely lies "between" those learnt during the unsupervised period.
The construction of conditional policies which efficiently and effectively generalize to latent codes not encountered during training is an open problem for such methods.
Our main contribution is to address this generalization and slow inference problem by making use of another recent advance in RL, successor features (Barreto et al., 2017) .
Successor features (SF) enable fast transfer learning between tasks that differ only in their reward function, which is assumed to be linear in some features.
Prior to this work, the automatic construction of these reward function features was an open research problem .
We show that, despite being previously cast as learning a policy space, behavioral mutual information (BMI) maximization provides a compelling solution to this feature learning problem.
Specifically, we show that the BMI objective can be adapted to learn precisely the features required by SF.
Together, these methods give rise to an algorithm, Variational Intrinsic Successor FeatuRes (VISR), which significantly improves performance in the RL with unsupervised pre-training scenario.
In order to illustrate the efficacy of the proposed method, we augment the popular 57-game Atari suite with such an unsupervised phase.
The use of this well-understood collection of tasks allows us to position our contribution more clearly against the current literature.
VISR achieves human-level performance on 12 games and outperforms all baselines, which includes algorithms that operate in three regimes: strictly unsupervised, supervised with limited data, and both.
Our results suggest that VISR is the first algorithm to achieve notable performance on the full Atari task suite in a setting of few-step RL with unsupervised pre-training, outperforming all baselines and buying performance equivalent to hundreds of millions of interaction steps compared to DQN on some games ( Figure 2c ).
As a suggestion for future investigations, the somewhat underwhelming results for the fully unsupervised version of VISR suggest that there is much room for improvement.
While curiosity-based methods are transient (i.e., asymptotically their intrinsic reward vanishes) and lack a fast adaptation mechanism, they do seem to encourage exploratory behavior slightly more than VISR.
A possible direction for future work would be to use a curiosity-based intrinsic reward inside of VISR, to encourage it to better explore the space of controllable policies.
Another interesting avenue for future investigation would be to combine the approach recently proposed by Ozair et al. (2019) to enforce the policies computed by VISR to be not only distinguishable but also far apart in a given metric space.
By using SFs on features that maximize BMI, we proposed an approach, VISR, that solves two open questions in the literature: how to compute features for the former and how to infer tasks in the latter.
Beyond the concrete method proposed here, we believe bridging the gap between BMI and SFs is an insightful contribution that may inspire other useful methods.
For convenience, we can refer to maximizing F(θ) as minimizing the loss function for parameters θ = (θ π , θ q ),
where θ π and θ q refer to the parameters of the policy π and variational approximation q, respectively.

assistant: text: We introduce Variational Intrinsic Successor FeatuRes (VISR), a novel algorithm which learns controllable features that can be leveraged to provide fast task inference through the successor features framework.