Paper:
Successor Features for Transfer in Reinforcement Learning
Transfer in reinforcement learning refers to the notion that generalization should occur not only within a task but also across tasks. We propose a transfer framework for the scenario where the reward function changes between tasks but the environment's dynamics remain the same. Our approach rests on two key ideas: successor features, a value function representation that decouples the dynamics of the environment from the rewards, and generalized policy improvement, a generalization of dynamic programming's policy improvement operation that considers a set of policies rather than a single one. Put together, the two ideas lead to an approach that integrates seamlessly within the reinforcement learning framework and allows the free exchange of information across tasks. The proposed method also provides performance guarantees for the transferred policy even before any learning has taken place. We derive two theorems that set our approach in firm theoretical ground and present experiments that show that it successfully promotes transfer in practice, significantly outperforming alternative methods in a sequence of navigation tasks and in the control of a simulated robotic arm.

Review:
This paper presents a RL optimization scheme and a theoretical analysis of its transfer performance. While the components of this work aren't novel, it combines them in an interesting, well-presented way that sheds new light.
The definition of transfer given in Lines 89–91 is nonstandard. It seems to be missing the assumption that t is not in T. The role of T' is a bit strange, making this a requirement for "additional transfer" rather than just transfer. It should be better clarified that this is a stronger requirement than transfer, and explained what it's good for — the paper shows this stronger property holds, but never uses it.
Among other prior work, Theorem 1 is closely related to Point-Based Value Iteration, and holds for the same reasons. In fact, w can be viewed as an unnormalized belief over which feature is important for the task (except that w can be negative).
The corollary in Lines 163–165 can be strengthened by relaxing the condition to hold for *some* s, s' that have positive occurrences.
The guarantee in (10) only comes from the closest w_j. Wouldn't it make sense to simplify and accelerate the algorithm by fixing this j at the beginning of the task? Or is there some benefit in practice beyond what the analysis shows? Empirical evidence either way would be helpful.
Very much missing is a discussion of the limitations of this approach. For example, how badly does it fail when the feature-space dimension becomes large?
Beyond the two 2D experiments presented, it's unclear how easy it is to find reward features such that similar tasks are close in feature-space. This seems to go to the heart of the challenge in RL, rather than to alleviate it.
The connection drawn to temporal abstraction and options is intriguing but lacking. While \psi is clearly related to control and w to goals, the important aspect of identifying option termination is missing here.