We develop a version of stochastic control that accounts for computational costs of inference. Past studies identified efficient coding without control, or efficient control that neglects the cost of synthesizing information. Here we combine these concepts into a framework where agents rationally approximate inference for efficient control. Specifically, we study Linear Quadratic Gaussian (LQG) control with an added internal cost on the relative precision of the posterior probability over the world state. This creates a trade-off: an agent can obtain more utility overall by sacrificing some task performance, if doing so saves enough bits during inference. We discover that the rational strategy that solves the joint inference and control problem goes through phase transitions depending on the task demands, switching from a costly but optimal inference to a family of suboptimal inferences related by rotation transformations, each misestimate the stability of the world. In all cases, the agent moves more to think less. This work provides a foundation for a new type of rational computations that could be used by both brains and machines for efficient but computationally constrained control.

翻译：我们提出了一种考虑推理计算成本的随机控制理论。以往的研究要么关注无控制的高效编码，要么关注忽略信息合成成本的高效控制。本文将这两个概念结合到一个框架中，在该框架中，智能体通过理性近似推理实现高效控制。具体而言，我们研究了线性二次高斯（LQG）控制，并在世界状态后验概率的相对精度上增加了一个内部成本。这产生了一个权衡：如果能在推理过程中节省足够的比特数，智能体可以通过牺牲部分任务性能来获得更高的总体效用。我们发现，解决联合推理与控制问题的理性策略会根据任务需求经历相变，从代价高昂但最优的推理切换到一系列通过旋转变换相关联的次优推理，每种次优推理都会错误估计世界的稳定性。在所有情况下，智能体通过更多行动来减少思考。这项工作为一种新型理性计算奠定了基础，这种计算可被大脑和机器用于实现高效但受计算资源约束的控制。