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The quintessential model-based reinforcement-learning agent iterativelyrefines its estimates or prior beliefs about the true underlying model of theenvironment. Recent empirical successes in model-based reinforcement learningwith function approximation, however, eschew the true model in favor of asurrogate that, while ignoring various facets of the environment, stillfacilitates effective planning over behaviors. Recently formalized as the valueequivalence principle, this algorithmic technique is perhaps unavoidable asreal-world reinforcement learning demands consideration of a simple,computationally-bounded agent interacting with an overwhelmingly complexenvironment. In this work, we entertain an extreme scenario wherein somecombination of immense environment complexity and limited agent capacityentirely precludes identifying an exactly value-equivalent model. In light ofthis, we embrace a notion of approximate value equivalence and introduce analgorithm for incrementally synthesizing simple and useful approximations ofthe environment from which an agent might still recover near-optimal behavior.Crucially, we recognize the information-theoretic nature of this lossyenvironment compression problem and use the appropriate tools ofrate-distortion theory to make mathematically precise how value equivalence canlend tractability to otherwise intractable sequential decision-making problems.

Between Rate-Distortion Theory & Value Equivalence in Model-Based Reinforcement Learning