# Data-driven Dynamic Multi-objective Optimal Control: An Aspiration-satisfying Reinforcement Learning Approach

arXiv: https://arxiv.org/abs/2005.07118 · HTML: https://mlsanity.com/paper/2005.07118/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2020.

## Built on by (most cited first, 5 of 5)

- [Assured Learning-enabled Autonomy: A Metacognitive Reinforcement Learning Framework](https://mlsanity.com/paper/2103.12558/) (2021)
- [Efficient Bayesian Policy Reuse with a Scalable Observation Model in Deep Reinforcement Learning](https://mlsanity.com/paper/2204.07729/) (2022)
- [A Risk-Averse Preview-based Q-Learning Algorithm: Application to Highway Driving of Autonomous Vehicles](https://mlsanity.com/paper/2112.03232/) (2021)
- [A Physics-Informed Learning Framework to Solve the Infinite-Horizon Optimal Control Problem](https://mlsanity.com/paper/2505.21842/) (2025)
- [RadDQN: a Deep Q Learning-based Architecture for Finding Time-efficient Minimum Radiation Exposure Pathway](https://mlsanity.com/paper/2402.00468/) (2024)

## Abstract (arXiv)

This paper presents an iterative data-driven algorithm for solving dynamic multi-objective (MO) optimal control problems arising in control of nonlinear continuous-time systems. It is first shown that the Hamiltonian functional corresponding to each objective can be leveraged to compare the performance of admissible policies. Hamiltonian-inequalities are then used for which their satisfaction guarantees satisfying the objectives' aspirations. An aspiration-satisfying dynamic optimization framework is then presented to optimize the main objective while satisfying the aspiration of other objectives. Relation to satisficing (good enough) decision-making framework is shown. A Sum-of-Square (SOS) based iterative algorithm is developed to solve the formulated aspiration-satisfying MO optimization. To obviate the requirement of complete knowledge of the system dynamics, a data-driven satisficing reinforcement learning approach is proposed to solve the SOS optimization problem in real-time using only the information of the system trajectories measured during a time interval without having full knowledge of the system dynamics. Finally, two simulation examples are provided to show the effectiveness of the proposed algorithm.