# Thinking Fast and Slow: Optimization Decomposition Across Timescales

arXiv: https://arxiv.org/abs/1704.07785 · HTML: https://mlsanity.com/paper/1704.07785/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2017.

## Built on by (most cited first, 30 of 60)

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- [The Quest for a Common Model of the Intelligent Decision Maker](https://mlsanity.com/paper/2202.13252/) (2022)
- [Thinking Fast and Slow in AI: the Role of Metacognition](https://mlsanity.com/paper/2110.01834/) (2021)
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- [Efficient Reinforcement Learning for Global Decision Making in the Presence of Local Agents at Scale](https://mlsanity.com/paper/2403.00222/) (2024)
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- [A conditional, a fuzzy and a probabilistic interpretation of self-organising maps](https://mlsanity.com/paper/2103.06854/) (2021)
- [Online Convex Optimization with Continuous Switching Constraint](https://mlsanity.com/paper/2103.11370/) (2021)
- [Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor](https://mlsanity.com/paper/2205.00741/) (2022)
- [Target Languages (vs. Inductive Biases) for Learning to Act and Plan](https://mlsanity.com/paper/2109.07195/) (2021)
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- [Combining Fast and Slow Thinking for Human-like and Efficient Navigation in Constrained Environments](https://mlsanity.com/paper/2201.07050/) (2022)

## Abstract (arXiv)

Many real-world control systems, such as the smart grid and human sensorimotor control systems, have decentralized components that react quickly using local information and centralized components that react slowly using a more global view. This paper seeks to provide a theoretical framework for how to design controllers that are decomposed across timescales in this way. The framework is analogous to how the network utility maximization framework uses optimization decomposition to distribute a global control problem across independent controllers, each of which solves a local problem; except our goal is to decompose a global problem temporally, extracting a timescale separation. Our results highlight that decomposition of a multi-timescale controller into a fast timescale, reactive controller and a slow timescale, predictive controller can be near-optimal in a strong sense. In particular, we exhibit such a design, named Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-timestep cost within a constant factor of the offline optimal in an adversarial setting.