The question of how to determine which states and actions are responsible for a certain outcome is known as the credit assignment problem and remains a central research question in reinforcement learning and artificial intelligence. Eligibility traces enable efficient credit assignment to the recent sequence of states and actions experienced by the agent, but not to counterfactual sequences that could also have led to the current state. In this work, we introduce expected eligibility traces. Expected traces allow, with a single update, to update states and actions that could have preceded the current state, even if they did not do so on this occasion. We discuss when expected traces provide benefits over classic (instantaneous) traces in temporal-difference learning, and show that some- times substantial improvements can be attained. We provide a way to smoothly interpolate between instantaneous and expected traces by a mechanism similar to bootstrapping, which ensures that the resulting algorithm is a strict generalisation of TD(λ). Finally, we discuss possible extensions and connections to related ideas, such as successor features.

In this work, we study value function approximation in reinforcement learning (RL) problems with high dimensional state or action spaces via a generalized version of representation policy iteration (RPI). We consider the limitations of proto-value functions (PVFs) at accurately approximating the value function in low dimensions and we highlight the importance of features learning for an improved low-dimensional value function approximation. Then, we adopt different representation learning algorithms on graphs to learn the basis functions that best represent the value function. We empirically show that node2vec, an algorithm for scalable feature learning in networks, and Graph Auto-Encoder constantly outperform the commonly used smooth proto-value functions in low-dimensional feature space.