Animals are able to rapidly infer from limited experience when sets of state action pairs have equivalent reward and transition dynamics. On the other hand, modern reinforcement learning systems must painstakingly learn through trial and error that sets of state action pairs are value equivalent -- requiring an often prohibitively large amount of samples from their environment. MDP homomorphisms have been proposed that reduce the observed MDP of an environment to an abstract MDP, which can enable more sample efficient policy learning. Consequently, impressive improvements in sample efficiency have been achieved when a suitable MDP homomorphism can be constructed a priori -- usually by exploiting a practioner's knowledge of environment symmetries. We propose a novel approach to constructing a homomorphism in discrete action spaces, which uses a partial model of environment dynamics to infer which state action pairs lead to the same state -- reducing the size of the state-action space by a factor equal to the cardinality of the action space. We call this method equivalent effect abstraction. In a gridworld setting, we demonstrate empirically that equivalent effect abstraction can improve sample efficiency in a model-free setting and planning efficiency for modelbased approaches. Furthermore, we show on cartpole that our approach outperforms an existing method for learning homomorphisms, while using 33x less training data.

Humans sometimes choose actions that they themselves can identify as sub-optimal, or wrong, even in the absence of additional information. How is this possible? We present an algorithmic theory of metacognition based on a well-understood trade-off in reinforcement learning (RL) between value-based RL and policy-based RL. To the cognitive (neuro)science community, our theory answers the outstanding question of why information can be used for error detection but not for action selection. To the machine learning community, our proposed theory creates a novel interaction between the Actor and Critic in Actor-Critic agents and notes a novel connection between RL and Bayesian Optimization. We call our proposed agent the Metacognitive Actor Critic (MAC). We conclude with showing how to create metacognition in machines by implementing a deep MAC and showing that it can detect (some of) its own suboptimal actions without external information or delay.