Thinking Fast and Slow: Optimization Decomposition Across Timescales

Thinking Fast and Slow: Optimization Decomposition Across Timescales

13 Nov 2017 | Gautam Goel, Niangjun Chen, Adam Wierman
This paper addresses the design of controllers for systems operating across multiple timescales, such as the smart grid and human sensorimotor control systems. It introduces a theoretical framework for decomposing a global control problem into independent controllers, one for fast reactions and one for slow, predictive actions. The framework is analogous to network utility maximization, where a global problem is distributed across independent controllers. The paper highlights that decomposing a multi-timescale controller into a fast, reactive controller and a slow, predictive controller can be nearly optimal in a strong sense. Specifically, it introduces Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-step cost within a constant factor of the offline optimal in an adversarial setting. The design of MRPC is motivated by a structural result about the offline optimal control action, which emphasizes a clear separation between fast and slow timescale controllers. This separation allows the slow controller to be sophisticated and predictive, while the fast controller is simple and reactive, making MRPC suitable for applications where the slow controller is centralized and the fast controllers are decentralized. The paper also discusses the hardness of multi-timescale control problems and provides a performance bound for MRPC, showing that it achieves near-optimal performance despite the simplicity of its fast controller and limited information about the future.This paper addresses the design of controllers for systems operating across multiple timescales, such as the smart grid and human sensorimotor control systems. It introduces a theoretical framework for decomposing a global control problem into independent controllers, one for fast reactions and one for slow, predictive actions. The framework is analogous to network utility maximization, where a global problem is distributed across independent controllers. The paper highlights that decomposing a multi-timescale controller into a fast, reactive controller and a slow, predictive controller can be nearly optimal in a strong sense. Specifically, it introduces Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-step cost within a constant factor of the offline optimal in an adversarial setting. The design of MRPC is motivated by a structural result about the offline optimal control action, which emphasizes a clear separation between fast and slow timescale controllers. This separation allows the slow controller to be sophisticated and predictive, while the fast controller is simple and reactive, making MRPC suitable for applications where the slow controller is centralized and the fast controllers are decentralized. The paper also discusses the hardness of multi-timescale control problems and provides a performance bound for MRPC, showing that it achieves near-optimal performance despite the simplicity of its fast controller and limited information about the future.
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Understanding Thinking fast and slow%3A Optimization decomposition across timescales