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 presents a theoretical framework for designing multi-timescale controllers that decompose control tasks across different timescales. The framework is inspired by network utility maximization, where optimization decomposition is used to distribute a global control problem across independent controllers. The goal is to decompose a global problem temporally, extracting a timescale separation. The authors show that decomposing a multi-timescale controller into a fast, reactive controller and a slow, predictive controller can be near-optimal in a strong sense. They introduce a new control policy called Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-timestep cost within a constant factor of the offline optimal in an adversarial setting. The paper discusses the challenges of multi-timescale control, where the dynamics of the system create tight coupling between timescales. This makes it difficult to achieve a clean separation between controllers at different timescales. The authors show that decomposition of a multi-timescale controller into a fast and slow controller is challenging without predictions. They prove that predictions are necessary to construct a constant competitive algorithm for multi-timescale control problems. The authors propose MRPC, a new multi-timescale control policy that consists of a simple, reflexive fast controller and a predictive slow controller. The fast controller performs no optimization or lookahead, while the slow controller handles the prediction and optimization. The design of MRPC is motivated by a structural result about the offline optimal control action, which highlights a strong decomposition between fast and slow timescale controllers. The paper provides strong guarantees on the performance of MRPC, showing that the per-step cost is at most a constant more than that of the offline optimal. This result is significant because it shows that even with limited information about the future, the policy can achieve near-optimal performance. The paper also discusses the implications of their results for real-world control systems, such as the smart grid, networking, and robotics.This paper presents a theoretical framework for designing multi-timescale controllers that decompose control tasks across different timescales. The framework is inspired by network utility maximization, where optimization decomposition is used to distribute a global control problem across independent controllers. The goal is to decompose a global problem temporally, extracting a timescale separation. The authors show that decomposing a multi-timescale controller into a fast, reactive controller and a slow, predictive controller can be near-optimal in a strong sense. They introduce a new control policy called Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-timestep cost within a constant factor of the offline optimal in an adversarial setting. The paper discusses the challenges of multi-timescale control, where the dynamics of the system create tight coupling between timescales. This makes it difficult to achieve a clean separation between controllers at different timescales. The authors show that decomposition of a multi-timescale controller into a fast and slow controller is challenging without predictions. They prove that predictions are necessary to construct a constant competitive algorithm for multi-timescale control problems. The authors propose MRPC, a new multi-timescale control policy that consists of a simple, reflexive fast controller and a predictive slow controller. The fast controller performs no optimization or lookahead, while the slow controller handles the prediction and optimization. The design of MRPC is motivated by a structural result about the offline optimal control action, which highlights a strong decomposition between fast and slow timescale controllers. The paper provides strong guarantees on the performance of MRPC, showing that the per-step cost is at most a constant more than that of the offline optimal. This result is significant because it shows that even with limited information about the future, the policy can achieve near-optimal performance. The paper also discusses the implications of their results for real-world control systems, such as the smart grid, networking, and robotics.
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