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.

我们开发了一种考虑推断计算成本的随机控制方法，结合了有效编码和高效控制的概念。研究发现，代理人通过在后验概率相对精度上增加内部成本来权衡总效用和任务性能，从而实现有效控制。通过研究线性二次高斯控制，我们发现代理人在不同任务需求下转换为一系列与旋转变换相关的次最优推断策略，每个策略都对世界的稳定性估计存在误差。这项工作为大脑和机器在高效但受计算限制的控制方面提供了新的合理计算基础。