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We present a new behavioural distance over the state space of a Markovdecision process, and demonstrate the use of this distance as an effectivemeans of shaping the learnt representations of deep reinforcement learningagents. While existing notions of state similarity are typically difficult tolearn at scale due to high computational cost and lack of sample-basedalgorithms, our newly-proposed distance addresses both of these issues. Inaddition to providing detailed theoretical analysis, we provide empiricalevidence that learning this distance alongside the value function yieldsstructured and informative representations, including strong results on theArcade Learning Environment benchmark.

MICo: Improved representations via sampling-based state similarity for Markov decision processes