# Local-Global Learning of Interpretable Control Policies: The Interface between MPC and Reinforcement Learning

arXiv: https://arxiv.org/abs/2503.13289 · HTML: https://mlsanity.com/paper/2503.13289/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 24 of its 64 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Plan Online, Learn Offline: Efficient Learning and Exploration via Model-Based Control](https://mlsanity.com/paper/1811.01848/) (2018)
- [Safe Reinforcement Learning Using Robust MPC](https://mlsanity.com/paper/1906.04005/) (2019)
- [Data-driven Economic NMPC using Reinforcement Learning](https://mlsanity.com/paper/1904.04152/) (2019)
- [Blending MPC & Value Function Approximation for Efficient Reinforcement Learning](https://mlsanity.com/paper/2012.05909/) (2020)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Deep Value Model Predictive Control](https://mlsanity.com/paper/1910.03358/) (2019)
- [Trust the Model Where It Trusts Itself -- Model-Based Actor-Critic with Uncertainty-Aware Rollout Adaption](https://mlsanity.com/paper/2405.19014/) (2024)
- [Learning for CasADi: Data-driven Models in Numerical Optimization](https://mlsanity.com/paper/2312.05873/) (2023)
- [Learning for MPC with Stability & Safety Guarantees](https://mlsanity.com/paper/2012.07369/) (2020)
- [PC-Gym: Benchmark Environments For Process Control Problems](https://mlsanity.com/paper/2410.22093/) (2024)
- [A view on learning robust goal-conditioned value functions: Interplay between RL and MPC](https://mlsanity.com/paper/2502.06996/) (2025)

## Built on by (most cited first, 1 of 1)

- [Model-free Reinforcement Learning for Model-based Control: Towards Safe, Interpretable and Sample-efficient Agents](https://mlsanity.com/paper/2507.13491/) (2025)

## Abstract (arXiv)

Making optimal decisions under uncertainty is a shared problem among distinct fields. While optimal control is commonly studied in the framework of dynamic programming, it is approached with differing perspectives of the Bellman optimality condition. In one perspective, the Bellman equation is used to derive a global optimality condition useful for iterative learning of control policies through interactions with an environment. Alternatively, the Bellman equation is also widely adopted to derive tractable optimization-based control policies that satisfy a local notion of optimality. By leveraging ideas from the two perspectives, we present a local-global paradigm for optimal control suited for learning interpretable local decision makers that approximately satisfy the global Bellman equation. The benefits and practical complications in local-global learning are discussed. These aspects are exemplified through case studies, which give an overview of two distinct strategies for unifying reinforcement learning and model predictive control. We discuss the challenges and trade-offs in these local-global strategies, towards highlighting future research opportunities for safe and optimal decision-making under uncertainty.