# Learning Convex Optimization Control Policies

arXiv: https://arxiv.org/abs/1912.09529 · HTML: https://mlsanity.com/paper/1912.09529/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2019.

## Built on by (most cited first, 30 of 31)

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- [Winning the CityLearn Challenge: Adaptive Optimization with Evolutionary Search under Trajectory-based Guidance](https://mlsanity.com/paper/2212.01939/) (2022)
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- [Data Sharing and Compression for Cooperative Networked Control](https://mlsanity.com/paper/2109.14675/) (2021)
- [Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces](https://mlsanity.com/paper/2208.08883/) (2022)
- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)
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- [Learning responsibility allocations for multi-agent interactions: A differentiable optimization approach with control barrier functions](https://mlsanity.com/paper/2410.07409/) (2024)
- [Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming](https://mlsanity.com/paper/2309.08700/) (2023)
- [Preference-Optimized Pareto Set Learning for Blackbox Optimization](https://mlsanity.com/paper/2408.09976/) (2024)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [Adaptive Road Configurations for Improved Autonomous Vehicle-Pedestrian Interactions using Reinforcement Learning](https://mlsanity.com/paper/2303.12289/) (2023)
- [Integrating Symbolic Reasoning into Neural Generative Models for Design Generation](https://mlsanity.com/paper/2310.09383/) (2023)
- [Leveraging Analytic Gradients in Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2506.01665/) (2025)
- [Performance-Driven Controller Tuning via Derivative-Free Reinforcement Learning](https://mlsanity.com/paper/2209.04854/) (2022)
- [LQGNet: Hybrid Model-Based and Data-Driven Linear Quadratic Stochastic Control](https://mlsanity.com/paper/2210.12803/) (2022)
- [Primitive Agentic First-Order Optimization](https://mlsanity.com/paper/2406.04841/) (2024)
- [Optimization Solution Functions as Deterministic Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2408.15368/) (2024)
- [Decision-Focused Learning for Complex System Identification: HVAC Management System Application](https://mlsanity.com/paper/2501.14708/) (2025)
- [End-to-End Learning-based Operation of Integrated Energy Systems for Buildings and Data Centers](https://mlsanity.com/paper/2604.14184/) (2026)
- [Differentiable Optimization Layers for Guaranteed Fairness in Deep Learning](https://mlsanity.com/paper/2605.17118/) (2026)

## Abstract (arXiv)

Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies (COCPs) include the linear quadratic regulator (LQR), convex model predictive control (MPC), and convex control-Lyapunov or approximate dynamic programming (ADP) policies. These types of control policies are tuned by varying the parameters in the optimization problem, such as the LQR weights, to obtain good performance, judged by application-specific metrics. Tuning is often done by hand, or by simple methods such as a crude grid search. In this paper we propose a method to automate this process, by adjusting the parameters using an approximate gradient of the performance metric with respect to the parameters. Our method relies on recently developed methods that can efficiently evaluate the derivative of the solution of a convex optimization problem with respect to its parameters. We illustrate our method on several examples.