Auxiliary tasks improve the representations learned by deep reinforcement learning agents. Analytically, their effect is reasonably well understood; in practice, however, their primary use remains in support of a main learning objective, rather than as a method for learning representations. This is perhaps surprising given that many auxiliary tasks are defined procedurally, and hence can be treated as an essentially infinite source of information about the environment. Based on this observation, we study the effectiveness of auxiliary tasks for learning rich representations, focusing on the setting where the number of tasks and the size of the agent's network are simultaneously increased. For this purpose, we derive a new family of auxiliary tasks based on the successor measure. These tasks are easy to implement and have appealing theoretical properties. Combined with a suitable off-policy learning rule, the result is a representation learning algorithm that can be understood as extending Mahadevan & Maggioni (2007)'s proto-value functions to deep reinforcement learning -- accordingly, we call the resulting object proto-value networks. Through a series of experiments on the Arcade Learning Environment, we demonstrate that proto-value networks produce rich features that may be used to obtain performance comparable to established algorithms, using only linear approximation and a small number (~4M) of interactions with the environment's reward function.

Many reinforcement learning algorithms use value functions to guide the search for better policies. These methods estimate the value of a single policy while generalizing across many states. The core idea of this paper is to flip this convention and estimate the value of many policies, for a single set of states. This approach opens up the possibility of performing direct gradient ascent in policy space without seeing any new data. The main challenge for this approach is finding a way to represent complex policies that facilitates learning and generalization. To address this problem, we introduce a scalable, differentiable fingerprinting mechanism that retains essential policy information in a concise embedding. Our empirical results demonstrate that combining these three elements (learned Policy Evaluation Network, policy fingerprints, gradient ascent) can produce policies that outperform those that generated the training data, in zero-shot manner.