Temporally Extended Successor Representations

We present a temporally extended variation of the successor representation, which we term t-SR. t-SR captures the expected state transition dynamics of temporally extended actions by constructing successor representations over primitive action repeats. This form of temporal abstraction does not learn a top-down hierarchy of pertinent task structures, but rather a bottom-up composition of coupled actions and action repetitions. This lessens the amount of decisions required in control without learning a hierarchical policy. As such, t-SR directly considers the time horizon of temporally extended action sequences without the need for predefined or domain-specific options. We show that in environments with dynamic reward structure, t-SR is able to leverage both the flexibility of the successor representation and the abstraction afforded by temporally extended actions. Thus, in a series of sparsely rewarded gridworld environments, t-SR optimally adapts learnt policies far faster than comparable value-based, model-free reinforcement learning methods. We also show that the manner in which t-SR learns to solve these tasks requires the learnt policy to be sampled consistently less often than non-temporally extended policies.