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Reinforcement learning algorithms typically rely on the assumption that the environment dynamics and value function can be expressed in terms of a Markovian state representation. However, when state information is only partially observable, how can an agent learn such a state representation, and how can it detect when it has found one? We introduce a metric that can accomplish both objectives, without requiring access to—or knowledge of—an underlying, unobservable state space. Our metric, the λ-discrepancy, is the difference between two distinct temporal difference (TD) value estimates, each computed using TD(λ) with a different value of λ. Since TD(λ=0) makes an implicit Markov assumption and TD(λ=1) does not, a discrepancy between these estimates is a potential indicator of a non-Markovian state representation. Indeed, we prove that the λ-discrepancy is exactly zero for all Markov decision processes and almost always non-zero for a broad class of partially observable environments. We also demonstrate empirically that, once detected, minimizing the λ-discrepancy can help with learning a memory function to mitigate the corresponding partial observability. We then train a reinforcement learning agent that simultaneously constructs two recurrent value networks with different λ parameters and minimizes the difference between them as an auxiliary loss. The approach scales to challenging partially observable domains, where the resulting agent frequently performs significantly better (and never performs worse) than a baseline recurrent agent with only a single value network. 

Deep Q-Network (DQN) is an algorithm that achieves human-level performance in complex domains like Atari games. One of the important elements of DQN is its use of a target network, which is necessary to stabilize learning. We argue that using a target network is incompatible with online reinforcement learning, and it is possible to achieve faster and more stable learning without a target network when we use Mellowmax, an alternative softmax operator. We derive novel properties of Mellowmax, and empirically show that the combination of DQN and Mellowmax, but without a target network, outperforms DQN with a target network. 

People often learn from others’ demonstrations, and inverse reinforcement learning (IRL) techniques have realized this capacity in machines. In contrast, teaching by demonstration has been less well studied computationally. Here, we develop a Bayesian model for teaching by demonstration. Stark differences arise when demonstrators are intentionally teaching (i.e. showing) a task versus simply performing (i.e. doing) a task. In two experiments, we show that human participants modify their teaching behavior consistent with the predictions of our model. Further, we show that even standard IRL algorithms benefit when learning from showing versus doing.